Solve (v^-5)^-5

$$( v ^ { - 5 } ) ^ { - 5 }$$

Evaluate

$$v^{25}$$

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

$$\left(v^{-5}\right)^{-5}$$

To raise a power to another power, multiply the exponents.

$$v^{-5\left(-5\right)}$$

Multiply -5 times -5.

$$v^{25}$$

Differentiate w.r.t. v

$$25v^{24}$$

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).

$$-5\left(v^{-5}\right)^{-5-1}\frac{\mathrm{d}}{\mathrm{d}v}(v^{-5})$$

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}.

$$-5\left(v^{-5}\right)^{-6}\left(-5\right)v^{-5-1}$$

Simplify.

$$25v^{-6}\left(v^{-5}\right)^{-6}$$