Solve 15x^6div5x^3

$$15 { x }^{ 6 } \div 5 { x }^{ 3 }$$

Evaluate

$$3x^{9}$$

Solution Steps

Divide 15x^{6} by 5 to get 3x^{6}.

$$3x^{6}x^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$3x^{9}$$

Differentiate w.r.t. x

$$27x^{8}$$

Steps Using Definition of a Derivative

Divide 15x^{6} by 5 to get 3x^{6}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{6}x^{3})$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{9})$$

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

$$9\times 3x^{9-1}$$

Multiply 9 times 3.

$$27x^{9-1}$$

Subtract 1 from 9.

$$27x^{8}$$