Solve 5{x}^frac{3{2}}+2{x}^frac{1{2}}-7x+3

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

Differentiate w.r.t. x

$$\frac{15\sqrt{x}}{2}-7+\frac{1}{\sqrt{x}}$$

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}.

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

Multiply \frac{3}{2} times 5.

$$\frac{15}{2}x^{\frac{3}{2}-1}+\frac{1}{2}\times 2x^{\frac{1}{2}-1}-7x^{1-1}$$

Subtract 1 from \frac{3}{2}.

$$\frac{15}{2}\sqrt{x}+\frac{1}{2}\times 2x^{\frac{1}{2}-1}-7x^{1-1}$$

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

$$\frac{15}{2}\sqrt{x}+x^{\frac{1}{2}-1}-7x^{1-1}$$

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

$$\frac{15}{2}\sqrt{x}+x^{-\frac{1}{2}}-7x^{1-1}$$

Subtract 1 from 1.

$$\frac{15}{2}\sqrt{x}+x^{-\frac{1}{2}}-7x^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{15}{2}\sqrt{x}+x^{-\frac{1}{2}}-7$$

Evaluate

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