Solve 8x^-5y^4/7x^-8y^-4

$$\frac { 8 x ^ { - 5 } y ^ { 4 } } { 7 x ^ { - 8 } y ^ { - 4 } }$$

Differentiate w.r.t. x

$$\frac{24x^{2}y^{8}}{7}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8y^{4}y^{4}}{7}x^{-5-\left(-8\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8y^{8}}{7}x^{3})$$

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}.

$$3\times \frac{8y^{8}}{7}x^{3-1}$$

Do the arithmetic.

$$\frac{24y^{8}}{7}x^{2}$$

Evaluate

$$\frac{8x^{3}y^{8}}{7}$$

Solution Steps

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

$$\frac{8x^{3}y^{8}}{7}$$