Solve c(3^3)^2=

$$c ( 3 ^ { 3 } ) ^ { 2 } =$$

Evaluate

$$729c$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$c\times 3^{6}$$

Calculate 3 to the power of 6 and get 729.

$$c\times 729$$

Differentiate w.r.t. c

$$729$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}c}(c\times 3^{6})$$

Calculate 3 to the power of 6 and get 729.

$$\frac{\mathrm{d}}{\mathrm{d}c}(c\times 729)$$

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

$$729c^{1-1}$$

Subtract 1 from 1.

$$729c^{0}$$

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

$$729\times 1$$

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

$$729$$