Solve sin(12x)+(x+4)-(x+4)

$$\sin ( 12x ) +(x+4)-(x+4)$$

Differentiate w.r.t. x

$$12\cos(12x)$$

Steps Using Chain Rule

To find the opposite of x+4, find the opposite of each term.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\sin(12x)+x+4-x-4)$$

Combine x and -x to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\sin(12x)+4-4)$$

Subtract 4 from 4 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\sin(12x))$$

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).

$$\cos(12x^{1})\frac{\mathrm{d}}{\mathrm{d}x}(12x^{1})$$

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}.

$$\cos(12x^{1})\times 12x^{1-1}$$

Simplify.

$$12\cos(12x^{1})$$

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

$$12\cos(12x)$$

Evaluate

$$\sin(12x)$$