Solve 3^0/a^-4

$$\frac { 3 ^ { 0 } } { a ^ { - 4 } }$$

Differentiate w.r.t. a

$$4a^{3}$$

Steps Using Chain Rule

Calculate 3 to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{a^{-4}})$$

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).

$$-\left(a^{-4}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}a}(a^{-4})$$

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}.

$$-\left(a^{-4}\right)^{-2}\left(-4\right)a^{-4-1}$$

Simplify.

$$4a^{-5}\left(a^{-4}\right)^{-2}$$

Evaluate

$$a^{4}$$

Solution Steps

Calculate 3 to the power of 0 and get 1.

$$\frac{1}{a^{-4}}$$