Solve 20x^15y^-7/30x^12y^13

$$\frac { 20 x ^ { 15 } y ^ { - 7 } } { 30 x ^ { 12 } y ^ { 13 } }$$

Evaluate

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

Solution Steps

Cancel out 10x^{12} in both numerator and denominator.

$$\frac{2y^{-7}x^{3}}{3y^{13}}$$

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

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

Differentiate w.r.t. x

$$\frac{2x^{2}}{y^{20}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{20}{y^{7}\times 30y^{13}}x^{15-12})$$

Do the arithmetic.

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

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}.

$$3\times \frac{2}{3y^{20}}x^{3-1}$$

Do the arithmetic.

$$\frac{2}{y^{20}}x^{2}$$