Solve 3x^4yz/-6xy^5

$$\frac { 3 x ^ { 4 } y z } { - 6 x y ^ { 5 } }$$

Differentiate w.r.t. x

$$-\frac{3zx^{2}}{2y^{4}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3yz}{-6y^{5}}x^{4-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{z}{2y^{4}}\right)x^{3})$$

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}.

$$3\left(-\frac{z}{2y^{4}}\right)x^{3-1}$$

Do the arithmetic.

$$\left(-\frac{3z}{2y^{4}}\right)x^{2}$$

Evaluate

$$-\frac{zx^{3}}{2y^{4}}$$

Solution Steps

Cancel out 3xy in both numerator and denominator.

$$\frac{zx^{3}}{-2y^{4}}$$