Evaluating the Derivative

The process of evaluating the derivative is essentially determining the rate of change of a function at any specific point. This critical calculus concept is usually denoted as f'(x) or dy/dx. There are several rules used to compute derivatives, including the power rule, product rule, quotient rule, and chain rule.

The problems about Evaluating the Derivative

Topic	Problem	Solution
None	Determine the rate of change on the interval $(3,…	Determine the rate of change on the interval $(3, 7)$ using the graph below:
None	Suppose $h (x) = 2 f (2 \tan (x)) + 2 f (6 + 3 \sin (x))$ .…	Suppose $h (x) = 2 f (2 \tan (x)) + 2 f (6 + 3 \sin (x))$ . You are also told that $f (0) = 40$ and \(f(6)=2…
None	If $f^{'} (x) = \frac{2}{x^{2}}$ then... A. $f(…	The question is asking for the antiderivative of the function $f^{'} (x) = \frac{2}{x^{2}}$ . Th…
None	Let $y = \tan (5 x + 2)$ . Find the differential $d y$ …	Given the function $y = \tan (5 x + 2)$ , we need to find the differential $d y$ when $x = 5$ and \…
None	If $f (x) = \sin^{- 1} (x)$ , then what is the value o…	Given the function $f (x) = \sin^{- 1} (x)$ , we need to find the derivative $f^{'} (x)$ and then evaluate …
None	14 Given $f(x)=x\left(1-3 x^{2}\right), f^{\prime…	Given the function $f (x) = x (1 - 3 x^{2})$ , we want to find $f^{'} (- 1)$ .
None	$f^{'} (2), f^{'} (x)$ ج \( f(x)=\lef…	$f^{'} (x) = \frac{3}{2} (x^{3} + 3 x^{2} - 3)^{\frac{1}{2}} \times (3 x^{2} + 6 x)$