Solve tan2x

$$\tan 2 x$$

Differentiate w.r.t. x

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

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).

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

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}.

$$\left(\sec(2x^{1})\right)^{2}\times 2x^{1-1}$$

Simplify.

$$2\left(\sec(2x^{1})\right)^{2}$$

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

$$2\left(\sec(2x)\right)^{2}$$

Evaluate

$$\tan(2x)$$