Question

Differentiate with respect to x,if y =4x^3.sinx

a. 4x^2(xcosx+sinx)

b. 4x^2(cosx+3sinx)

c. 4x^2(xcosx+3sinx)

d. 4x^2(xcosx−3sinx)

Answer 1

Answer on Question #47076 – Math – Differential Calculus | Equations

Question:

Differentiate with respect to $x$, if $y = 4x^3 \cdot \sin x$

a. $4x^2(x \cos x + \sin x)$

b. $4x^2(\cos x + 3 \sin x)$

c. $4x^2(x \cos x + 3 \sin x)$

d. $4x^2(x \cos x - 3 \sin x)$

Solution:

The product rule: For the functions $f$ and $g$, the derivative of the function $h(x) = f(x)g(x)$ with respect to $x$ is the following:

$$h'(x) = f(x)g'(x) + f'(x)g(x)$$

Therefore:

$$\begin{array}{l} y' = 4x^3(\sin x)' + (4x^3)'\sin x = 4x^3\cos x + 4 \cdot 3x^2\sin x \\ = 4x^2(x\cos x + 3\sin x) \end{array}$$

Answer: c. $4x^2(x\cos x + 3\sin x)$

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