Solve -48x^2yz^2/64x^3y^2z

$$\frac { - 48 x ^ { 2 } y z ^ { 2 } } { 64 x ^ { 3 } y ^ { 2 } z }$$

Differentiate w.r.t. x

$$\frac{3z}{4yx^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{48yz^{2}}{64zy^{2}}\right)x^{2-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{3z}{4y}\right)\times \frac{1}{x})$$

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}.

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

Do the arithmetic.

$$\frac{3z}{4y}x^{-2}$$

Evaluate

$$-\frac{3z}{4xy}$$

Solution Steps

Cancel out 16yzx^{2} in both numerator and denominator.

$$\frac{-3z}{4xy}$$