Solve 2x^{2}*(x^3divx^-2/x^2divx^-3)

$$2 x ^ { 2 } \times ( \frac { x ^ { 3 } \div x ^ { - 2 } } { x ^ { 2 } \div x ^ { - 3 } } )$$

Evaluate

$$2x^{2}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -2 from 3 to get 5.

$$2x^{2}\times \frac{x^{5}}{\frac{x^{2}}{x^{-3}}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -3 from 2 to get 5.

$$2x^{2}\times \frac{x^{5}}{x^{5}}$$

Divide x^{5} by x^{5} to get 1.

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

Multiply 2 and 1 to get 2.

$$2x^{2}$$

Differentiate w.r.t. x

$$4x$$

Steps Using Definition of a Derivative

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -2 from 3 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}\times \frac{x^{5}}{\frac{x^{2}}{x^{-3}}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -3 from 2 to get 5.

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

Divide x^{5} by x^{5} to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}\times 1)$$

Multiply 2 and 1 to get 2.

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

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

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

Multiply 2 times 2.

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

Subtract 1 from 2.

$$4x^{1}$$

For any term t, t^{1}=t.

$$4x$$