Solve x^0,5/x^-0,7

$$\frac { x ^ { 0,5 } } { x ^ { - 0,7 } }$$

Differentiate w.r.t. x

$$\frac{6\sqrt[5]{x}}{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1}x^{0,5-\left(-0,7\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{1,2})$$

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}.

$$1,2x^{1,2-1}$$

Do the arithmetic.

$$1,2\sqrt[5]{x}$$

Evaluate

$$x^{1,2}$$