Solve 6x^3div3x

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

Evaluate

$$2x^{4}$$

Solution Steps

Divide 6x^{3} by 3 to get 2x^{3}.

$$2x^{3}x$$

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

$$2x^{4}$$

Differentiate w.r.t. x

$$8x^{3}$$

Steps Using Definition of a Derivative

Divide 6x^{3} by 3 to get 2x^{3}.

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

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

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

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

$$4\times 2x^{4-1}$$

Multiply 4 times 2.

$$8x^{4-1}$$

Subtract 1 from 4.

$$8x^{3}$$