Solve gamma^2*2^2

$$\gamma ^ { 2 \times 2 ^ { 2 } }$$

Evaluate

$$\gamma ^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\gamma ^{2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\gamma ^{8}$$

Differentiate w.r.t. γ

$$8\gamma ^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}\gamma }(\gamma ^{2^{3}})$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\mathrm{d}}{\mathrm{d}\gamma }(\gamma ^{8})$$

The derivative of ax^{n} is nax^{n-1}.

$$8\gamma ^{8-1}$$

Subtract 1 from 8.

$$8\gamma ^{7}$$