Question

sin³(2x+3),Find the derivative of the given function defined on proper domains.

Answer 1

it is given that function, f(x) = sin³(2x + 3)
we have to find the derivative of the given function.

f(x) = sin³(2x + 3)

differentiate with respect to x,

df(x)/dx = d{sin³(2x + 3)}/dx

= 3sin²(2x + 3) × d{sin(2x + 3)}/dx

= 3sin²(2x + 3) × cos(2x + 3) × d{(2x+3)}/dx

= 3sin²(2x + 3)cos(2x + 3) × 2

= 6sin²(2x + 3)cos(2x + 3)

hence, first order derivative of the given function is 6sin²(2x + 3)cos(2x + 3)

Answer 2

Dear Student,

Solution:

We know that in derivative , we first differentiate function's power ,

then given trigonometric function,
then (2x+3)

By this way

$\frac{d}{dx} {sin}^{3} (2x + 3) \\ \\ = 3 \: {sin}^{2} (2x + 3) \: \frac{d}{dx} sin(2x + 3) \\ \\ = 3 \: {sin}^{2} (2x + 3) \: cos(2x + 3) \: \frac{d}{dx} (2x + 3) \\ \\ = 3 \: {sin}^{2} (2x + 3) \: cos(2x + 3) \:(2) \\ \\ = 6{sin}^{2} (2x + 3) \: cos(2x + 3)$
is the final answer.

Hope it helps you