Solve 3a^3*4a^4

$$3 a ^ { 3 } \cdot 4 a ^ { 4 }$$

Evaluate

$$12a^{7}$$

Solution Steps

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

$$3a^{7}\times 4$$

Multiply 3 and 4 to get 12.

$$12a^{7}$$

Differentiate w.r.t. a

$$84a^{6}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(3a^{7}\times 4)$$

Multiply 3 and 4 to get 12.

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

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

$$7\times 12a^{7-1}$$

Multiply 7 times 12.

$$84a^{7-1}$$

Subtract 1 from 7.

$$84a^{6}$$