Solve f(n)=sinpix

$$f ( n ) = \sin \pi x$$

Differentiate w.r.t. x

$$\pi \cos(\pi x)$$

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).

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

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}.

$$\cos(\pi x^{1})\pi x^{1-1}$$

Simplify.

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

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

$$\pi \cos(\pi x)$$

Evaluate

$$\sin(\pi x)$$