Solve sin(90-θ)

$$\sin ( 90 - \theta )$$

Differentiate w.r.t. θ

$$-\cos(90-\theta )$$

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).

$$\cos(-\theta ^{1}+90)\frac{\mathrm{d}}{\mathrm{d}\theta }(-\theta ^{1}+90)$$

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}.

$$\cos(-\theta ^{1}+90)\left(-1\right)\theta ^{1-1}$$

Simplify.

$$-\cos(-\theta ^{1}+90)$$

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

$$-\cos(-\theta +90)$$

Evaluate

$$\sin(90-\theta )$$