Solve frac{5x(3sqrt{x})^2}{5xsqrt{x}}

$$\frac { 5 x ( 3 \sqrt { x } ) ^ { 2 } } { 5 x \sqrt { x } }$$

Differentiate w.r.t. x

$$\frac{9}{2\sqrt{x}}$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9\sqrt{x}x^{0})$$

For any number a except 0, a^{0}=1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9\sqrt{x})$$

The derivative of a constant term is 0.

$$0$$

Evaluate

$$9\sqrt{x}$$