Solve 4x^2y^5/x^7

$$\frac { 4 x ^ { 2 } y ^ { 5 } } { x ^ { 7 } }$$

Differentiate w.r.t. x

$$-\frac{20y^{5}}{x^{6}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4y^{5}}{1}x^{2-7})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$\left(-20y^{5}\right)x^{-6}$$

Evaluate

$$4\times \left(\frac{y}{x}\right)^{5}$$

Solution Steps

Cancel out x^{2} in both numerator and denominator.

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