Solve frac{14xy^frac{1{3}}}{2x^frac{3{4}}z^-6}

$$\frac { 14 x y ^ { \frac { 1 } { 3 } } } { 2 x ^ { \frac { 3 } { 4 } } z ^ { - 6 } }$$

Differentiate w.r.t. x

$$\frac{7\sqrt[3]{y}z^{6}}{4x^{\frac{3}{4}}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{14\sqrt[3]{y}z^{6}}{2}x^{1-\frac{3}{4}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7\sqrt[3]{y}z^{6}\sqrt[4]{x})$$

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}.

$$\frac{1}{4}\times 7\sqrt[3]{y}z^{6}x^{\frac{1}{4}-1}$$

Do the arithmetic.

$$\frac{7\sqrt[3]{y}z^{6}}{4}x^{-\frac{3}{4}}$$

Evaluate

$$7\sqrt[4]{x}\sqrt[3]{y}z^{6}$$