Solve x^2/x^-9

$$\frac { x ^ { 2 } } { x ^ { - 9 } }$$

Differentiate w.r.t. x

$$11x^{10}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1}x^{2-\left(-9\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{11})$$

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}.

$$11x^{11-1}$$

Do the arithmetic.

$$11x^{10}$$

Evaluate

$$x^{11}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -9 from 2 to get 11.

$$x^{11}$$