Solve 2g^3*4g^4

$$2 g ^ { 3 } \times 4 g ^ { 4 }$$

Evaluate

$$8g^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$2g^{7}\times 4$$

Multiply 2 and 4 to get 8.

$$8g^{7}$$

Differentiate w.r.t. g

$$56g^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}g}(2g^{7}\times 4)$$

Multiply 2 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}g}(8g^{7})$$

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

$$7\times 8g^{7-1}$$

Multiply 7 times 8.

$$56g^{7-1}$$

Subtract 1 from 7.

$$56g^{6}$$