Solve cos(2θ)

$$\cos ( 2 \theta )$$

Differentiate w.r.t. θ

$$-2\sin(2\theta )$$

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).

$$\left(-\sin(2\theta ^{1})\right)\frac{\mathrm{d}}{\mathrm{d}\theta }(2\theta ^{1})$$

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}.

$$\left(-\sin(2\theta ^{1})\right)\times 2\theta ^{1-1}$$

Simplify.

$$-2\sin(2\theta ^{1})$$

For any term t, t^{1}=t.

$$-2\sin(2\theta )$$

Evaluate

$$\cos(2\theta )$$