Solve 2x^3*2x^4/(x^3)^-1

$$\frac { 2 x ^ { 3 } \cdot 2 x ^ { 4 } } { ( x ^ { 3 } ) ^ { - 1 } }$$

Evaluate

$$4x^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{2x^{7}\times 2}{\left(x^{3}\right)^{-1}}$$

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

$$\frac{2x^{7}\times 2}{x^{-3}}$$

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

$$2\times 2x^{10}$$

Multiply 2 and 2 to get 4.

$$4x^{10}$$

Differentiate w.r.t. x

$$40x^{9}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{7}\times 2}{\left(x^{3}\right)^{-1}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{7}\times 2}{x^{-3}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2\times 2x^{10})$$

Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{10})$$

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

$$10\times 4x^{10-1}$$

Multiply 10 times 4.

$$40x^{10-1}$$

Subtract 1 from 10.

$$40x^{9}$$