Solve frac{-3x^{-4}y^{6}z^-7}{2x^3y^6z^-1}

$$\frac { - 3 x ^ { - 4 } y ^ { 6 } z ^ { - 7 } } { 2 x ^ { 3 } y ^ { 6 } z ^ { - 1 } }$$

Evaluate

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

Solution Steps

Cancel out y^{6} in both numerator and denominator.

$$\frac{-3z^{-7}x^{-4}}{2\times \frac{1}{z}x^{3}}$$

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

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

Differentiate w.r.t. x

$$\frac{21}{2z^{6}x^{8}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(-\frac{3y^{6}}{z^{7}}\right)z}{2y^{6}}x^{-4-3})$$

Do the arithmetic.

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

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}.

$$-7\left(-\frac{3}{2z^{6}}\right)x^{-7-1}$$

Do the arithmetic.

$$\frac{21}{2z^{6}}x^{-8}$$