Derivative Formulas

Apply the constant factor and power rules of differentiation to find the first derivative of each of the following functions. In each case take the derivative with respect to the independent variable suggested by the expression on the right side of the equal sign. Make sure that you assign the proper name to the derivative function. Please note that there is no need to employ either the quotient r…

Apply the constant factor and power rules of differentiation to find the first derivative of each of the following functions. In each case take the derivative with respect to the independent variable suggested by the expression on the right side of the equal sign. Make sure that you assign the proper name to the derivative function. Please note that there is no need to employ either the quotient r…

Apply the constant factor and product rules of differentiation to find the first derivative of each of the following functions. Write out the Leibniz notation for the product rule as applied to the given function. In each case take the derivative with respect to the independent variable suggested by the expression on the right side of the equal sign. Make sure that you assign the proper name to th…

Apply the constant factor and product rules of differentiation to find the first derivative of each of the following functions. Write out the Leibniz notation for the product rule as applied to the given function. In each case take the derivative with respect to the independent variable suggested by the expression on the right side of the equal sign. Make sure that you assign the proper name to th…

Apply the constant factor and product rules of differentiation to find the first derivative of each of the following functions. Write out the Leibniz notation for the product rule as applied to the given function. In each case take the derivative with respect to the independent variable suggested by the expression on the right side of the equal sign. Make sure that you assign the proper name to th…

Apply the constant factor and product rules of differentiation to find the first derivative of each of the following functions. Write out the Leibniz notation for the product rule as applied to the given function. In each case take the derivative with respect to the independent variable suggested by the expression on the right side of the equal sign. Make sure that you assign the proper name to th…

Apply the constant factor and product rules of differentiation to find the first derivative of each of the following functions. Write out the Leibniz notation for the product rule as applied to the given function. In each case take the derivative with respect to the independent variable suggested by the expression on the right side of the equal sign. Make sure that you assign the proper name to th…

Apply the constant factor and product rules of differentiation to find the first derivative of each of the following functions. Write out the Leibniz notation for the product rule as applied to the given function. In each case take the derivative with respect to the independent variable suggested by the expression on the right side of the equal sign. Make sure that you assign the proper name to th…

Apply the constant factor and quotient rules of differentiation to find the first derivative of each of the following functions. Write out the Leibniz notation for the quotient rule as applied to the given function. In each case take the derivative with respect to the independent variable suggested by the expression on the right side of the equal sign. Make sure that you assign the proper name to…

Apply the constant factor and quotient rules of differentiation to find the first derivative of each of the following functions. Write out the Leibniz notation for the quotient rule as applied to the given function. In each case take the derivative with respect to the independent variable suggested by the expression on the right side of the equal sign. Make sure that you assign the proper name to…

Apply the constant factor and quotient rules of differentiation to find the first derivative of each of the following functions. Write out the Leibniz notation for the quotient rule as applied to the given function. In each case take the derivative with respect to the independent variable suggested by the expression on the right side of the equal sign. Make sure that you assign the proper name to…

Apply the constant factor and quotient rules of differentiation to find the first derivative of each of the following functions. Write out the Leibniz notation for the quotient rule as applied to the given function. In each case take the derivative with respect to the independent variable suggested by the expression on the right side of the equal sign. Make sure that you assign the proper name to…

Apply the constant factor and quotient rules of differentiation to find the first derivative of each of the following functions. Write out the Leibniz notation for the quotient rule as applied to the given function. In each case take the derivative with respect to the independent variable suggested by the expression on the right side of the equal sign. Make sure that you assign the proper name to…

Multiple applications of the product rule are required when finding the derivative formula of the product of three of more functions. After simplification, however, the predictable pattern shown below emerges.

Apply the product rule twice to the expression $\lzoo{x}{\fe{f}{x}\fe{g}{x}\fe{h}{x}}$ to verify the formula stated above for the product of three functions. The first application of the product rule is shown below to help you ge…

Multiple applications of the product rule are required when finding the derivative formula of the product of three of more functions. After simplification, however, the predictable pattern shown below emerges.

Apply the formula shown for the product of four functions to determine the derivative with respect to $x$ of the function $p$ defined by $\fe{p}{x}=x^2e^x\fe{\sin}{x}\fe{\cos}{x}$.

Find the first derivative with respect to $x$ for each of the following functions and for each function find the equation of the tangent line at the stated value of $x$. Make sure that you use appropriate techniques of differentiation.

$\fe{f}{x}=\dfrac{x^3+x^2}{x}$; tangent line at $5$

Find the first derivative with respect to $x$ for each of the following functions and for each function find the equation of the tangent line at the stated value of $x$. Make sure that you use appropriate techniques of differentiation.

$\fe{h}{x}=\dfrac{x}{1+x}$; tangent line at $-2$

Find the first derivative with respect to $x$ for each of the following functions and for each function find the equation of the tangent line at the stated value of $x$. Make sure that you use appropriate techniques of differentiation.

$\fe{K}{x}=\dfrac{1+x}{2x+2}$; tangent line at $8$

Find the equation of the tangent line to $\fd{f}$ at $\pi$ if $\fe{f}{x}=\fe{\sin}{2x}$.