Solve x^frac{13{7}}div(x^frac{8{7}}divx^frac{6{7}})

$$x ^ { \frac { 13 } { 7 } } \div ( x ^ { \frac { 8 } { 7 } } \div x ^ { \frac { 6 } { 7 } } )$$

Differentiate w.r.t. x

$$\frac{11x^{\frac{4}{7}}}{7}$$

Steps Using Definition of a Derivative

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract \frac{6}{7} from \frac{8}{7} to get \frac{2}{7}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{\frac{13}{7}}}{x^{\frac{2}{7}}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract \frac{2}{7} from \frac{13}{7} to get \frac{11}{7}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{\frac{11}{7}})$$

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

$$\frac{11}{7}x^{\frac{11}{7}-1}$$

Subtract 1 from \frac{11}{7}.

$$\frac{11}{7}x^{\frac{4}{7}}$$

Evaluate

$$x^{\frac{11}{7}}$$