Solve -32x^2y^2z/4xz

$$\frac{ -32 { x }^{ 2 } { y }^{ 2 } z }{ 4xz }$$

Differentiate w.r.t. x

$$-8y^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{32zy^{2}}{4z}\right)x^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-8y^{2}\right)x^{1})$$

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}.

$$\left(-8y^{2}\right)x^{1-1}$$

Do the arithmetic.

$$\left(-8y^{2}\right)x^{0}$$

For any term t except 0, t^{0}=1.

$$\left(-8y^{2}\right)\times 1$$

For any term t, t\times 1=t and 1t=t.

$$-8y^{2}$$

Evaluate

$$-8xy^{2}$$

Solution Steps

Cancel out 4xz in both numerator and denominator.

$$-8xy^{2}$$