Solve (5a^3)(7a^9)

$$( 5 a ^ { 3 } ) ( 7 a ^ { 9 } )$$

Evaluate

$$35a^{12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 9 to get 12.

$$5a^{12}\times 7$$

Multiply 5 and 7 to get 35.

$$35a^{12}$$

Differentiate w.r.t. a

$$420a^{11}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 9 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}a}(5a^{12}\times 7)$$

Multiply 5 and 7 to get 35.

$$\frac{\mathrm{d}}{\mathrm{d}a}(35a^{12})$$

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

$$12\times 35a^{12-1}$$

Multiply 12 times 35.

$$420a^{12-1}$$

Subtract 1 from 12.

$$420a^{11}$$