Solve 10{x}^frac{3{5}}-{x}^frac{7{2}}+6{x}^frac{8{3}}-3

$$10 { x }^{ \frac{ 3 }{ 5 } } - { x }^{ \frac{ 7 }{ 2 } } +6 { x }^{ \frac{ 8 }{ 3 } } -3$$

Differentiate w.r.t. x

$$-\frac{7x^{\frac{5}{2}}}{2}+16x^{\frac{5}{3}}+\frac{6}{x^{\frac{2}{5}}}$$

Steps Using Derivative Rule for Sum

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}.

$$\frac{3}{5}\times 10x^{\frac{3}{5}-1}+\frac{7}{2}\left(-1\right)x^{\frac{7}{2}-1}+\frac{8}{3}\times 6x^{\frac{8}{3}-1}$$

Multiply \frac{3}{5} times 10.

$$6x^{\frac{3}{5}-1}+\frac{7}{2}\left(-1\right)x^{\frac{7}{2}-1}+\frac{8}{3}\times 6x^{\frac{8}{3}-1}$$

Subtract 1 from \frac{3}{5}.

$$6x^{-\frac{2}{5}}+\frac{7}{2}\left(-1\right)x^{\frac{7}{2}-1}+\frac{8}{3}\times 6x^{\frac{8}{3}-1}$$

Multiply \frac{7}{2} times -1.

$$6x^{-\frac{2}{5}}-\frac{7}{2}x^{\frac{7}{2}-1}+\frac{8}{3}\times 6x^{\frac{8}{3}-1}$$

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

$$6x^{-\frac{2}{5}}-\frac{7}{2}x^{\frac{5}{2}}+\frac{8}{3}\times 6x^{\frac{8}{3}-1}$$

Multiply \frac{7}{2} times -1.

$$6x^{-\frac{2}{5}}-\frac{7}{2}x^{\frac{5}{2}}+16x^{\frac{8}{3}-1}$$

Subtract 1 from \frac{8}{3}.

$$6x^{-\frac{2}{5}}-\frac{7}{2}x^{\frac{5}{2}}+16x^{\frac{5}{3}}$$

Evaluate

$$-x^{\frac{7}{2}}+6x^{\frac{8}{3}}+10x^{\frac{3}{5}}-3$$