Solve frac{10x^{5}y^-6z^7}{5x^-3z^-2}

$$\frac { 10 x ^ { 5 } y ^ { - 6 } z ^ { 7 } } { 5 x ^ { - 3 } z ^ { - 2 } }$$

Evaluate

$$\frac{2x^{8}z^{9}}{y^{6}}$$

Solution Steps

Cancel out 5 in both numerator and denominator.

$$\frac{2y^{-6}x^{5}z^{7}}{x^{-3}z^{-2}}$$

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

$$2y^{-6}x^{8}z^{9}$$

Differentiate w.r.t. x

$$\frac{16x^{7}z^{9}}{y^{6}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{10z^{7}}{y^{6}\times \frac{5}{z^{2}}}x^{5-\left(-3\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2z^{9}}{y^{6}}x^{8})$$

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}.

$$8\times \frac{2z^{9}}{y^{6}}x^{8-1}$$

Do the arithmetic.

$$\frac{16z^{9}}{y^{6}}x^{7}$$