Solve 15x^4/5x^2

$$\frac{ 15 { x }^{ 4 } }{ 5 } { x }^{ 2 }$$

Evaluate

$$3x^{6}$$

Solution Steps

Divide 15x^{4} by 5 to get 3x^{4}.

$$3x^{4}x^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$3x^{6}$$

Differentiate w.r.t. x

$$18x^{5}$$

Steps Using Definition of a Derivative

Divide 15x^{4} by 5 to get 3x^{4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{4}x^{2})$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

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

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

$$6\times 3x^{6-1}$$

Multiply 6 times 3.

$$18x^{6-1}$$

Subtract 1 from 6.

$$18x^{5}$$