Solve sinF_{2}4

$$\sin F _ { 2 } 4$$

Differentiate w.r.t. F_2

$$4\cos(4F_{2})$$

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).

$$\cos(4F_{2}^{1})\frac{\mathrm{d}}{\mathrm{d}F_{2}}(4F_{2}^{1})$$

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}.

$$\cos(4F_{2}^{1})\times 4F_{2}^{1-1}$$

Simplify.

$$4\cos(4F_{2}^{1})$$

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

$$4\cos(4F_{2})$$

Evaluate

$$\sin(4F_{2})$$