Solve 2sqrt{5}c*5sqrt{5}

$$2 \sqrt { 5 } c \cdot 5 \sqrt { 5 }$$

Evaluate

$$50c$$

Solution Steps

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$2\times 5\times 5c$$

Multiply 2 and 5 to get 10.

$$10\times 5c$$

Multiply 10 and 5 to get 50.

$$50c$$

Differentiate w.r.t. c

$$50$$

Steps Using Definition of a Derivative

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}c}(2\times 5\times 5c)$$

Multiply 2 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}c}(10\times 5c)$$

Multiply 10 and 5 to get 50.

$$\frac{\mathrm{d}}{\mathrm{d}c}(50c)$$

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

$$50c^{1-1}$$

Subtract 1 from 1.

$$50c^{0}$$

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

$$50\times 1$$

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

$$50$$