Solve 120x^2y^3z^5/30x^3y{z^2}

$$\frac{ 120 { x }^{ 2 } { y }^{ 3 } { z }^{ 5 } }{ 30 { x }^{ 3 } y { z }^{ 2 } }$$

Differentiate w.r.t. x

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{120y^{3}z^{5}}{30yz^{2}}x^{2-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4y^{2}z^{3}\times \frac{1}{x})$$

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}.

$$-4y^{2}z^{3}x^{-1-1}$$

Do the arithmetic.

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

Evaluate

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

Solution Steps

Cancel out 30yx^{2}z^{2} in both numerator and denominator.

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