Solve sin(x^4*2x)

$$\sin ( { x }^{ 4 } \times 2x )$$

Differentiate w.r.t. x

$$10x^{4}\cos(2x^{5})$$

Steps Using Chain Rule

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\sin(x^{5}\times 2))$$

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).

$$\cos(2x^{5})\frac{\mathrm{d}}{\mathrm{d}x}(2x^{5})$$

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}.

$$\cos(2x^{5})\times 5\times 2x^{5-1}$$

Simplify.

$$10x^{4}\cos(2x^{5})$$

Evaluate

$$\sin(2x^{5})$$