Solve 11a^3*33a^4

$$11 a ^ { 3 } \cdot 33 a ^ { 4 }$$

Evaluate

$$363a^{7}$$

Solution Steps

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

$$11a^{7}\times 33$$

Multiply 11 and 33 to get 363.

$$363a^{7}$$

Differentiate w.r.t. a

$$2541a^{6}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(11a^{7}\times 33)$$

Multiply 11 and 33 to get 363.

$$\frac{\mathrm{d}}{\mathrm{d}a}(363a^{7})$$

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

$$7\times 363a^{7-1}$$

Multiply 7 times 363.

$$2541a^{7-1}$$

Subtract 1 from 7.

$$2541a^{6}$$