Solve x^{0}*(x^2)^3div(x^2*x^1/2)

$$x ^ { 0 } \times ( x ^ { 2 } ) ^ { 3 } \div ( x ^ { 2 } \times x ^ { 1 / 2 } )$$

Differentiate w.r.t. x

$$\frac{7x^{\frac{5}{2}}}{2}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{0}x^{6}}{x^{2}x^{\frac{1}{2}}})$$

To multiply powers of the same base, add their exponents. Add 0 and 6 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{6}}{x^{2}x^{\frac{1}{2}}})$$

To multiply powers of the same base, add their exponents. Add 2 and \frac{1}{2} to get \frac{5}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{6}}{x^{\frac{5}{2}}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract \frac{5}{2} from 6 to get \frac{7}{2}.

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

The derivative of ax^{n} is nax^{n-1}.

$$\frac{7}{2}x^{\frac{7}{2}-1}$$

Subtract 1 from \frac{7}{2}.

$$\frac{7}{2}x^{\frac{5}{2}}$$

Evaluate

$$x^{\frac{7}{2}}$$