Solve -52x^3y^2z/13xy^2=

$$\frac { - 52 x ^ { 3 } y ^ { 2 } z } { 13 x y ^ { 2 } } =$$

Differentiate w.r.t. x

$$-8xz$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{52zy^{2}}{13y^{2}}\right)x^{3-1})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

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

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

$$\left(-8z\right)x$$

Evaluate

$$-4zx^{2}$$

Solution Steps

Cancel out 13xy^{2} in both numerator and denominator.

$$-4zx^{2}$$