Solve frac{sqrt{x}x^frac{3{5}}x^frac{2{5}}}{x^-frac{1{4}}}

$$\frac { \sqrt { x } x ^ { \frac { 3 } { 5 } } x ^ { \frac { 2 } { 5 } } } { x ^ { - \frac { 1 } { 4 } } }$$

Differentiate w.r.t. x

$$\frac{7x^{\frac{3}{4}}}{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{\frac{2}{5}}\sqrt{x}}{1}x^{\frac{3}{5}-\left(-\frac{1}{4}\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{\frac{9}{10}}x^{\frac{17}{20}})$$

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}.

$$\frac{17}{20}x^{\frac{9}{10}}x^{\frac{17}{20}-1}$$

Do the arithmetic.

$$\frac{17x^{\frac{9}{10}}}{20}x^{-\frac{3}{20}}$$

Evaluate

$$x^{\frac{7}{4}}$$