Finding the Derivative Using Product Rule

In calculus, the product rule is a technique employed to determine the derivative of the multiplication of two or more functions. It asserts that the derivative of the product of two functions is the result of the first function and the derivative of the second function added to the second function and the derivative of the first.

The problems about Finding the Derivative Using Product Rule

Topic	Problem	Solution
None	Calculate $\frac{d y}{d x}$ . You need not expand …	Given the function $y = (3 x^{2} + x) (x - x^{2})$ .
None	Differentiate. $f (x) = x^{6} \ln 5 x$	The given function is a product of two functions, $x^{6}$ and $\ln (5 x)$ .
None	Find the derivative of the function $y=(4 x+5)^{4…	Given the function $y = (4 x + 5)^{4} (3 x + 1)^{- 2}$
None	Find dy/dt. 3) $y = t^{4} {(t^{5} + 3)}^{4}$	We are given the function $y = t^{4} (t^{5} + 3)^{4}$ and we are asked to find $\frac{d y}{d t}$ .
None	$\begin{array}{l}f(x)=\left(4 x^{2}+6\right)^{6}\…	Given the function $f (x) = (4 x^{2} + 6)^{6} (3 x^{2} + 6)^{11}$ , we are asked to find its derivative \(f'…
None	Suppose $f (x) = x^{2} p (x)$ for some unknown functi…	Given that $f (x) = x^{2} p (x)$ , we can find the derivative of $f (x)$ using the product rule.
None	Find $\frac{d y}{d x}$ \[ y=6(\tan x+\sec x)(\tan…	Given the function $y = 6 (\tan x + \sec x) (\tan x - \sec x)$
None	a. Apply the Product Rule. Let $u=\left(2 x^{2}+3…	Let $u = 2 x^{2} + 3$ and $v = 8 x + 5 + \frac{1}{x}$
None	Find $y^{'}$ by (a) applying the Product Rul…	First, we recognize that the given function can be written in the form $(a + b) (c + d + e)$ , where \(a=…
None	(b) Let $A (x) = (x - 2)^{2} (3 x - 4)^{2}$ Find $A^{\pri…	Let $A (x) = (x - 2)^{2} (3 x - 4)^{2}$
None	20 Consider $f (x) = \frac{1}{100} (3 x - 5) (5 x + 21)$ a…	$f (x) = \frac{1}{100} (3 x - 5) (5 x + 21)$