Solve 6w+7w^1/2-20-0

$$6 w + 7 w ^ { 1 / 2 } - 20 - 0$$

Evaluate

$$6w+7\sqrt{w}-20$$

Solution Steps

Multiply -1 and 0 to get 0.

$$6w+7w^{\frac{1}{2}}-20+0$$

Add -20 and 0 to get -20.

$$6w+7w^{\frac{1}{2}}-20$$

Differentiate w.r.t. w

$$6+\frac{7}{2\sqrt{w}}$$

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}.

$$6w^{1-1}+\frac{1}{2}\times 7w^{\frac{1}{2}-1}$$

Subtract 1 from 1.

$$6w^{0}+\frac{1}{2}\times 7w^{\frac{1}{2}-1}$$

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

$$6w^{0}+\frac{7}{2}w^{\frac{1}{2}-1}$$

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

$$6w^{0}+\frac{7}{2}w^{-\frac{1}{2}}$$

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

$$6\times 1+\frac{7}{2}w^{-\frac{1}{2}}$$

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

$$6+\frac{7}{2}w^{-\frac{1}{2}}$$