Solve 15x^3div45x=

$$15 { x }^{ 3 } \div 45x=$$

Evaluate

$$\frac{x^{4}}{3}$$

Solution Steps

Divide 15x^{3} by 45 to get \frac{1}{3}x^{3}.

$$\frac{1}{3}x^{3}x$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{1}{3}x^{4}$$

Differentiate w.r.t. x

$$\frac{4x^{3}}{3}$$

Steps Using Definition of a Derivative

Divide 15x^{3} by 45 to get \frac{1}{3}x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{3}x^{3}x)$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{3}x^{4})$$

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

$$4\times \frac{1}{3}x^{4-1}$$

Multiply 4 times \frac{1}{3}.

$$\frac{4}{3}x^{4-1}$$

Subtract 1 from 4.

$$\frac{4}{3}x^{3}$$