Solve (4x^-3y^3)/8x^2y^-1=

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

Evaluate

$$\frac{y^{4}}{2x^{5}}$$

Solution Steps

Cancel out 4 in both numerator and denominator.

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

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

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

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

$$\frac{y^{4}}{2x^{5}}$$

Differentiate w.r.t. x

$$-\frac{5y^{4}}{2x^{6}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4y^{3}y}{8}x^{-3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{y^{4}}{2}x^{-5})$$

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}.

$$-5\times \frac{y^{4}}{2}x^{-5-1}$$

Do the arithmetic.

$$\left(-\frac{5y^{4}}{2}\right)x^{-6}$$