Solve (5x^8/10x^-3y

$$( \frac { 5 x ^ { 8 } } { 10 x ^ { - 3 } y }$$

Evaluate

$$\frac{x^{11}}{2y}$$

Solution Steps

Cancel out 5 in both numerator and denominator.

$$\frac{x^{8}}{2x^{-3}y}$$

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

$$\frac{x^{11}}{2y}$$

Differentiate w.r.t. x

$$\frac{11x^{10}}{2y}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{10y}x^{8-\left(-3\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2y}x^{11})$$

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}.

$$11\times \frac{1}{2y}x^{11-1}$$

Do the arithmetic.

$$\frac{11}{2y}x^{10}$$