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

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

Evaluate

$$\frac{3}{5x^{\frac{7}{4}}}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 2 from \frac{1}{4}.

$$\frac{3^{1}x^{-\frac{7}{4}}}{5^{1}}$$

Divide 3 by 5.

$$\frac{3}{5}x^{-\frac{7}{4}}$$

Differentiate w.r.t. x

$$-\frac{21}{20x^{\frac{11}{4}}}$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{5}x^{-\frac{7}{4}})$$

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}.

$$-\frac{7}{4}\times \frac{3}{5}x^{-\frac{7}{4}-1}$$

Do the arithmetic.

$$-\frac{21}{20}x^{-\frac{11}{4}}$$