Solve frac{-80x^{4}y^{5}z^3}{60x^2y^5z^2}

$$\frac { - 80 x ^ { 4 } y ^ { 5 } z ^ { 3 } } { 60 x ^ { 2 } y ^ { 5 } z ^ { 2 } }$$

Differentiate w.r.t. x

$$-\frac{8xz}{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{80z^{3}y^{5}}{60z^{2}y^{5}}\right)x^{4-2})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$\left(-\frac{8z}{3}\right)x^{1}$$

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

$$\left(-\frac{8z}{3}\right)x$$

Evaluate

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

Solution Steps

Cancel out 20x^{2}z^{2}y^{5} in both numerator and denominator.

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