Solve 4x^4x^-8/8x^-7y^-2

$$\frac { 4 x ^ { 4 } x ^ { - 8 } } { 8 x ^ { - 7 } y ^ { - 2 } }$$

Evaluate

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

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and -8 to get -4.

$$\frac{4x^{-4}}{8x^{-7}y^{-2}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{x^{-4}}{2x^{-7}y^{-2}}$$

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

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

Differentiate w.r.t. x

$$\frac{3\left(xy\right)^{2}}{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{x^{8}\times \frac{8}{y^{2}}}x^{4-\left(-7\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{y^{2}}{2x^{8}}x^{11})$$

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}.

$$11\times \frac{y^{2}}{2x^{8}}x^{11-1}$$

Do the arithmetic.

$$\frac{11y^{2}}{2x^{8}}x^{10}$$