Solve x^2yz^7/x^-1y^11z

$$\frac { x ^ { 2 } y z ^ { 7 } } { x ^ { - 1 } y ^ { 11 } z }$$

Evaluate

$$\frac{x^{3}z^{6}}{y^{10}}$$

Solution Steps

Cancel out yz in both numerator and denominator.

$$\frac{x^{2}z^{6}}{\frac{1}{x}y^{10}}$$

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

$$\frac{x^{3}z^{6}}{y^{10}}$$

Differentiate w.r.t. x

$$\frac{3x^{2}z^{6}}{y^{10}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{yz^{7}}{zy^{11}}x^{2-\left(-1\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{z^{6}}{y^{10}}x^{3})$$

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}.

$$3\times \frac{z^{6}}{y^{10}}x^{3-1}$$

Do the arithmetic.

$$\frac{3z^{6}}{y^{10}}x^{2}$$