Solve 20x^5/30x^2y^3

$$\frac { 20 x ^ { 5 } } { 30 x ^ { 2 } y ^ { 3 } }$$

Differentiate w.r.t. x

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{20}{30y^{3}}x^{5-2})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

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

Evaluate

$$\frac{2\times \left(\frac{x}{y}\right)^{3}}{3}$$

Solution Steps

Cancel out 10x^{2} in both numerator and denominator.

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