Solve -3x^7yz^3/-10x^2y^-3{z^2}=

$$\frac{ -3 { x }^{ 7 } y { z }^{ 3 } }{ -10 { x }^{ 2 } { y }^{ -3 } { z }^{ 2 } } =$$

Evaluate

$$\frac{3zy^{4}x^{5}}{10}$$

Solution Steps

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

$$\frac{-3yzx^{5}}{-10y^{-3}}$$

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

$$\frac{-3zy^{4}x^{5}}{-10}$$

Differentiate w.r.t. x

$$\frac{3z\left(xy\right)^{4}}{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{3yz^{3}}{-\frac{10z^{2}}{y^{3}}}\right)x^{7-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3zy^{4}}{10}x^{5})$$

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}.

$$5\times \frac{3zy^{4}}{10}x^{5-1}$$

Do the arithmetic.

$$\frac{3zy^{4}}{2}x^{4}$$