Solve -2x^5y^7/-6x^-2y^5

$$\frac { - 2 x ^ { 5 } y ^ { 7 } } { - 6 x ^ { - 2 } y ^ { 5 } }$$

Evaluate

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

Solution Steps

Cancel out 2y^{5} in both numerator and denominator.

$$\frac{-y^{2}x^{5}}{-3x^{-2}}$$

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

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

Differentiate w.r.t. x

$$\frac{7y^{2}x^{6}}{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{2y^{7}}{-6y^{5}}\right)x^{5-\left(-2\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{y^{2}}{3}x^{7})$$

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}.

$$7\times \frac{y^{2}}{3}x^{7-1}$$

Do the arithmetic.

$$\frac{7y^{2}}{3}x^{6}$$