Solve d/dxleft(left(sin(2x^2)right)^1right)

$$\frac{d}{d x } \left( { \left( \sin ( 2 { x }^{ 2 } ) \right) }^{ 1 } \right)$$

Evaluate

$$4x\cos(2x^{2})$$

Steps Using Chain Rule

Calculate \sin(2x^{2}) to the power of 1 and get \sin(2x^{2}).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\sin(2x^{2}))$$

If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

$$\cos(2x^{2})\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$\cos(2x^{2})\times 2\times 2x^{2-1}$$

Simplify.

$$4x\cos(2x^{2})$$

Differentiate w.r.t. x

$$4\left(-4x^{2}\sin(2x^{2})+\cos(2x^{2})\right)$$