Solve -12x^3y^3z/3x^4y^

$$\frac{ -12 { x }^{ 3 } { y }^{ 3 } z }{ 3 { x }^{ 4 } { y }^{ } }$$

Differentiate w.r.t. x

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{12zy^{3}}{3y^{1}}\right)x^{3-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-4zy^{2}\right)\times \frac{1}{x})$$

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}.

$$-\left(-4zy^{2}\right)x^{-1-1}$$

Do the arithmetic.

$$4zy^{2}x^{-2}$$

Evaluate

$$-\frac{4zy^{2}}{x}$$

Solution Steps

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

$$\frac{-4zy^{2}}{x}$$