Solve [pi/picos(pix)]_1^2

$$[ \frac { \pi } { \pi } \cos ( \pi x ) ] _ { 1 } ^ { 2 }$$

Differentiate w.r.t. x

$$-\pi \sin(\pi x)$$

Steps Using Chain Rule

Divide \pi by \pi to get 1.

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

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).

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

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}.

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

Simplify.

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

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

$$\left(-\pi \right)\sin(\pi x)$$

Evaluate

$$\cos(\pi x)$$