Solve -6x^3y^5/3x^6y^-1

$$\frac { - 6 x ^ { 3 } y ^ { 5 } } { 3 x ^ { 6 } y ^ { - 1 } }$$

Evaluate

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

Solution Steps

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

$$\frac{-2y^{5}}{\frac{1}{y}x^{3}}$$

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

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

Differentiate w.r.t. x

$$\frac{6y^{6}}{x^{4}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(-6y^{5}\right)y}{3}x^{3-6})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-2y^{6}\right)x^{-3})$$

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}.

$$-3\left(-2y^{6}\right)x^{-3-1}$$

Do the arithmetic.

$$6y^{6}x^{-4}$$