Solve 6f^4_{2}12f^4

$$6 f ^ { 4 } _ { 2 } 12 f ^ { 4 }$$

Evaluate

$$72f^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$6f^{8}\times 12$$

Multiply 6 and 12 to get 72.

$$72f^{8}$$

Differentiate w.r.t. f

$$576f^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}f}(6f^{8}\times 12)$$

Multiply 6 and 12 to get 72.

$$\frac{\mathrm{d}}{\mathrm{d}f}(72f^{8})$$

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

$$8\times 72f^{8-1}$$

Multiply 8 times 72.

$$576f^{8-1}$$

Subtract 1 from 8.

$$576f^{7}$$