Find the derivative of the following function.
A)
B)
C)
D)
E)

Question

​Find the derivative of the following function. ​  ​
A) ​ 
B) ​ 
C) ​ 
D) ​ 
E) ​

Quizplus · Accepted Answer

The given function is in the form of $h(x)=f(g(x))$. Chain rule states that the derivative of such a function is $h'(x)=f'(g(x))g'(x)$. Applying chain rule to the given function, we get
$$\frac{d}{dx}\left((2x^3+3)^3\right)\cdot \frac{d}{dx}\left((6x+11)^{\frac{1}{3}}\right)$$
Using power rule and chain rule respectively, we get
$$36(2x^3+3)^2\cdot \frac{1}{3}(6x+11)^{-\frac{2}{3}}\cdot 6$$
Simplifying this expression further, we get
$$\frac{72(2x^3+3)^2}{(6x+11)^{\frac{2}{3}}}$$
which is the derivative of the given function. Therefore, the correct answer is (D).

​Find the Derivative of the Following Function

Find the Derivative of the Following Function