Solve sqrt[5]{3^5}quadc)

$$\sqrt[ 5 ] { 3 ^ { 5 } } \quad c )$$

Evaluate

$$3c$$

Solution Steps

Calculate 3 to the power of 5 and get 243.

$$\sqrt[5]{243}c$$

Calculate \sqrt[5]{243} and get 3.

$$3c$$

Differentiate w.r.t. c

$$3$$

Steps Using Definition of a Derivative

Calculate 3 to the power of 5 and get 243.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\sqrt[5]{243}c)$$

Calculate \sqrt[5]{243} and get 3.

$$\frac{\mathrm{d}}{\mathrm{d}c}(3c)$$

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

$$3c^{1-1}$$

Subtract 1 from 1.

$$3c^{0}$$

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

$$3\times 1$$

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

$$3$$