Solve 8x^4y^-8/4x^-1y^3

$$\frac { 8 x ^ { 4 } y ^ { - 8 } } { 4 x ^ { - 1 } y ^ { 3 } }$$

Evaluate

$$\frac{2x^{5}}{y^{11}}$$

Solution Steps

Cancel out 4 in both numerator and denominator.

$$\frac{2y^{-8}x^{4}}{\frac{1}{x}y^{3}}$$

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

$$\frac{2y^{-8}x^{5}}{y^{3}}$$

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

$$\frac{2x^{5}}{y^{11}}$$

Differentiate w.r.t. x

$$\frac{10x^{4}}{y^{11}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8}{y^{8}\times 4y^{3}}x^{4-\left(-1\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{y^{11}}x^{5})$$

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}.

$$5\times \frac{2}{y^{11}}x^{5-1}$$

Do the arithmetic.

$$\frac{10}{y^{11}}x^{4}$$