Solve 56x^3yz^4/48x^5y^2{z^}

$$\frac{ 56 { x }^{ 3 } y { z }^{ 4 } }{ 48 { x }^{ 5 } { y }^{ 2 } { z }^{ } }$$

Differentiate w.r.t. x

$$-\frac{7\times \left(\frac{z}{x}\right)^{3}}{3y}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{56yz^{4}}{48z^{1}y^{2}}x^{3-5})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7z^{3}}{6y}x^{-2})$$

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}.

$$-2\times \frac{7z^{3}}{6y}x^{-2-1}$$

Do the arithmetic.

$$\left(-\frac{7z^{3}}{3y}\right)x^{-3}$$

Evaluate

$$\frac{7z^{3}}{6yx^{2}}$$

Solution Steps

Cancel out 8yzx^{3} in both numerator and denominator.

$$\frac{7z^{3}}{6yx^{2}}$$