Question

d/dx sin³x=........,Select Proper option from the given options.
(a) 3sin²x
(b) 3cos²x
(c) 3sin²x cosx
(d) -3cos²x sinx

Answer 1

In the attachment I have answered this problem.                  I have applied chain rule to find the derivative of the given function.                    See the attachment for detailed solution.

Answer 2

we have to find the value of d/dx sin³x

we know,
$\bf{\frac{d(sinx)}{dx}=cosx}$

$\bf{\frac{d(f(x)^n)}{dx}=nf(x)^{n-1}\frac{df(x)}{dx}}$

so, d/dx sin³x = 3sin^(3 - 1)x d(sinx)/dx

= 3sin²x × cosx

= 3sin²x.cosx

hence, option (c) is correct