Solve 15x^4:3x^2=

$$15 x ^ { 4 } : 3 x ^ { 2 } =$$

Evaluate

$$5x^{6}$$

Solution Steps

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

$$5x^{4}x^{2}$$

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

$$5x^{6}$$

Differentiate w.r.t. x

$$30x^{5}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{4}x^{2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{6})$$

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

$$6\times 5x^{6-1}$$

Multiply 6 times 5.

$$30x^{6-1}$$

Subtract 1 from 6.

$$30x^{5}$$