Solve 3^2t-3t

$$3 ^ { 2 } t - 3 t$$

Evaluate

$$6t$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$9t-3t$$

Combine 9t and -3t to get 6t.

$$6t$$

Differentiate w.r.t. t

$$6$$

Steps Using Definition of a Derivative

Calculate 3 to the power of 2 and get 9.

$$\frac{\mathrm{d}}{\mathrm{d}t}(9t-3t)$$

Combine 9t and -3t to get 6t.

$$\frac{\mathrm{d}}{\mathrm{d}t}(6t)$$

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

$$6t^{1-1}$$

Subtract 1 from 1.

$$6t^{0}$$

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

$$6\times 1$$

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

$$6$$