Solve x^3y^7a^6/x^4y

$$\frac { x ^ { 3 } y ^ { 7 } a ^ { 6 } } { x ^ { 4 } y }$$

Differentiate w.r.t. x

$$-\frac{\left(ay\right)^{6}}{x^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{a^{6}y^{7}}{y}x^{3-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(a^{6}y^{6}\times \frac{1}{x})$$

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}.

$$-a^{6}y^{6}x^{-1-1}$$

Do the arithmetic.

$$\left(-a^{6}y^{6}\right)x^{-2}$$

Evaluate

$$\frac{\left(ay\right)^{6}}{x}$$

Solution Steps

Cancel out yx^{3} in both numerator and denominator.

$$\frac{a^{6}y^{6}}{x}$$