Solve 3^3v/sqrt{1}

$$\frac { 3 ^ { 3 } v } { \sqrt { 1 } }$$

Evaluate

$$27v$$

Solution Steps

Calculate 3 to the power of 3 and get 27.

$$\frac{27v}{\sqrt{1}}$$

Calculate the square root of 1 and get 1.

$$\frac{27v}{1}$$

Anything divided by one gives itself.

$$27v$$

Differentiate w.r.t. v

$$27$$

Steps Using Definition of a Derivative

Calculate 3 to the power of 3 and get 27.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{27v}{\sqrt{1}})$$

Calculate the square root of 1 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{27v}{1})$$

Anything divided by one gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}v}(27v)$$

The derivative of ax^{n} is nax^{n-1}.

$$27v^{1-1}$$

Subtract 1 from 1.

$$27v^{0}$$

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

$$27\times 1$$

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

$$27$$