Solve cos2x(30+4)

$$\cos 2 x ( 30 + 4 )$$

Differentiate w.r.t. x

$$-68\sin(68x)$$

Steps Using Chain Rule

Add 30 and 4 to get 34.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\cos(2x\times 34))$$

Multiply 2 and 34 to get 68.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\cos(68x))$$

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).

$$\left(-\sin(68x^{1})\right)\frac{\mathrm{d}}{\mathrm{d}x}(68x^{1})$$

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}.

$$\left(-\sin(68x^{1})\right)\times 68x^{1-1}$$

Simplify.

$$-68\sin(68x^{1})$$

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

$$-68\sin(68x)$$

Evaluate

$$\cos(68x)$$