Solve vsqrt[3]{27}-sqrt{100}

$$v \sqrt[ 3 ] { 27 } - \sqrt { 100 }$$

Evaluate

$$3v-10$$

Solution Steps

Calculate \sqrt[3]{27} and get 3.

$$v\times 3-\sqrt{100}$$

Calculate the square root of 100 and get 10.

$$v\times 3-10$$

Differentiate w.r.t. v

$$3$$

Steps Using Derivative Rule for Sum

Calculate \sqrt[3]{27} and get 3.

$$\frac{\mathrm{d}}{\mathrm{d}v}(v\times 3-\sqrt{100})$$

Calculate the square root of 100 and get 10.

$$\frac{\mathrm{d}}{\mathrm{d}v}(v\times 3-10)$$

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}.

$$3v^{1-1}$$

Subtract 1 from 1.

$$3v^{0}$$

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

$$3\times 1$$

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

$$3$$