Question

differentiate f(x) =cos^3(x^2)​

Answer 1

Step-by-step explanation:

3cos^2(2x)

hoga x^2 ka 2x hoga

Answer 2

given function, f(x) = cos³(x²)

we have to differentiate f(x) with respect to x.

we know, if any function, y = f(x)ⁿ is given then, differentiation of y is dy/dx = d(f(x))ⁿ)/dx = n.f(x)^(n-1) × d(f(x))/dx

similarly, given function , f(x) = cos³(x²) = (cosx²)³

then, dy/dx = d{(cosx²)³}/dx

= 3.(cosx²)² × d(cosx²)/dx

= 3cos²x² × [-sinx² × d(x²)/dx ] [ as we know, differentiation of cosα = -sinα ]

= -3cos²x². sinx² . 2x

hence, differentiation of cos³(x²) = - 3cos²x². sinx² . 2x