Solve 2x^3/(x^-1)^36/3

$$\frac { 2 x ^ { 3 } } { ( x ^ { - 1 } ) ^ { 3 } } \frac { 6 } { 3 }$$

Evaluate

$$4x^{6}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -1 and 3 to get -3.

$$\frac{2x^{3}}{x^{-3}}\times \frac{6}{3}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$2x^{6}\times \frac{6}{3}$$

Divide 6 by 3 to get 2.

$$2x^{6}\times 2$$

Multiply 2 and 2 to get 4.

$$4x^{6}$$

Differentiate w.r.t. x

$$24x^{5}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply -1 and 3 to get -3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{3}}{x^{-3}}\times \frac{6}{3})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{6}\times \frac{6}{3})$$

Divide 6 by 3 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{6}\times 2)$$

Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{6})$$

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

$$6\times 4x^{6-1}$$

Multiply 6 times 4.

$$24x^{6-1}$$

Subtract 1 from 6.

$$24x^{5}$$