Solve d/dxsin(x^2)

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

Evaluate

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

Steps Using Chain Rule

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).

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

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}.

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

Simplify.

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

Differentiate w.r.t. x

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