Solve 4a^4*7a^5

$$4 a ^ { 4 } \cdot 7 a ^ { 5 }$$

Evaluate

$$28a^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$4a^{9}\times 7$$

Multiply 4 and 7 to get 28.

$$28a^{9}$$

Differentiate w.r.t. a

$$252a^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}a}(4a^{9}\times 7)$$

Multiply 4 and 7 to get 28.

$$\frac{\mathrm{d}}{\mathrm{d}a}(28a^{9})$$

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

$$9\times 28a^{9-1}$$

Multiply 9 times 28.

$$252a^{9-1}$$

Subtract 1 from 9.

$$252a^{8}$$