Solve 3x3^3

$$3x { 3 }^{ 3 }$$

Evaluate

$$81x$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$3^{4}x$$

Calculate 3 to the power of 4 and get 81.

$$81x$$

Differentiate w.r.t. x

$$81$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3^{4}x)$$

Calculate 3 to the power of 4 and get 81.

$$\frac{\mathrm{d}}{\mathrm{d}x}(81x)$$

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

$$81x^{1-1}$$

Subtract 1 from 1.

$$81x^{0}$$

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

$$81\times 1$$

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

$$81$$