Solve frac{-5x^{11}y^{14}z^6}{60x^2y^3z^2}

$$\frac { - 5 x ^ { 11 } y ^ { 14 } z ^ { 6 } } { 60 x ^ { 2 } y ^ { 3 } z ^ { 2 } }$$

Differentiate w.r.t. x

$$-\frac{3z^{4}x^{8}y^{11}}{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{5z^{6}y^{14}}{60z^{2}y^{3}}\right)x^{11-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{z^{4}y^{11}}{12}\right)x^{9})$$

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}.

$$9\left(-\frac{z^{4}y^{11}}{12}\right)x^{9-1}$$

Do the arithmetic.

$$\left(-\frac{3z^{4}y^{11}}{4}\right)x^{8}$$

Evaluate

$$-\frac{z^{4}x^{9}y^{11}}{12}$$

Solution Steps

Cancel out 5x^{2}z^{2}y^{3} in both numerator and denominator.

$$\frac{-z^{4}x^{9}y^{11}}{12}$$