Solve frac{2x^-frac{7{4}}}{4x^frac{4{3}}}

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

Evaluate

$$\frac{1}{2x^{\frac{37}{12}}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

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

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

$$\frac{1}{2x^{\frac{37}{12}}}$$

Differentiate w.r.t. x

$$-\frac{37}{24x^{\frac{49}{12}}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{4}x^{-\frac{7}{4}-\frac{4}{3}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x^{-\frac{37}{12}})$$

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}.

$$-\frac{37}{12}\times \frac{1}{2}x^{-\frac{37}{12}-1}$$

Do the arithmetic.

$$-\frac{37}{24}x^{-\frac{49}{12}}$$