Solve 12a^4*4a^3

$$12 a ^ { 4 } \times 4 a ^ { 3 }$$

Evaluate

$$48a^{7}$$

Solution Steps

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

$$12a^{7}\times 4$$

Multiply 12 and 4 to get 48.

$$48a^{7}$$

Differentiate w.r.t. a

$$336a^{6}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(12a^{7}\times 4)$$

Multiply 12 and 4 to get 48.

$$\frac{\mathrm{d}}{\mathrm{d}a}(48a^{7})$$

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

$$7\times 48a^{7-1}$$

Multiply 7 times 48.

$$336a^{7-1}$$

Subtract 1 from 7.

$$336a^{6}$$