Solve 2x+7x^frac{1{2}}-4

$$2 x + 7 x ^ { \frac { 1 } { 2 } } - 4$$

Differentiate w.r.t. x

$$2+\frac{7}{2\sqrt{x}}$$

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}.

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

Subtract 1 from 1.

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

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

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

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

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

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

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

For any term t, t\times 1=t and 1t=t.

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

Evaluate

$$2x+7\sqrt{x}-4$$