Solve 4(f^2)^4

$$4 ( f ^ { 2 } ) ^ { 4 }$$

Differentiate w.r.t. f

$$32f^{7}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}f}(4f^{8})$$

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

$$8\times 4f^{8-1}$$

Multiply 8 times 4.

$$32f^{8-1}$$

Subtract 1 from 8.

$$32f^{7}$$

Evaluate

$$4f^{8}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$4f^{8}$$