Solve 9a^4div3a^7quad1)

$$9 a ^ { 4 } \div 3 a ^ { 7 } \quad 1 )$$

Evaluate

$$3a^{11}$$

Solution Steps

Divide 9a^{4} by 3 to get 3a^{4}.

$$3a^{4}a^{7}\times 1$$

To multiply powers of the same base, add their exponents. Add 4 and 7 to get 11.

$$3a^{11}\times 1$$

Multiply 3 and 1 to get 3.

$$3a^{11}$$

Differentiate w.r.t. a

$$33a^{10}$$

Steps Using Definition of a Derivative

Divide 9a^{4} by 3 to get 3a^{4}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3a^{4}a^{7}\times 1)$$

To multiply powers of the same base, add their exponents. Add 4 and 7 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3a^{11}\times 1)$$

Multiply 3 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3a^{11})$$

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

$$11\times 3a^{11-1}$$

Multiply 11 times 3.

$$33a^{11-1}$$

Subtract 1 from 11.

$$33a^{10}$$