Solve x^10/x^-5

$$\frac { x ^ { 10 } } { x ^ { - 5 } }$$

Differentiate w.r.t. x

$$15x^{14}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1}x^{10-\left(-5\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{15})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$15x^{15-1}$$

Do the arithmetic.

$$15x^{14}$$

Evaluate

$$x^{15}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -5 from 10 to get 15.

$$x^{15}$$