Solve d/dt(tt+2)e^-05t)

$$\frac { d } { d t } ( t t + 2 ) e ^ { - 05 t } )$$

Evaluate

$$2t$$

Steps Using Derivative Rule for Sum

Multiply t and t to get t^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\left(t^{2}+2\right)e^{0\times 5t})$$

Multiply 0 and 5 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\left(t^{2}+2\right)e^{0t})$$

Anything times zero gives zero.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\left(t^{2}+2\right)e^{0})$$

Calculate e to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\left(t^{2}+2\right)\times 1)$$

Use the distributive property to multiply t^{2}+2 by 1.

$$\frac{\mathrm{d}}{\mathrm{d}t}(t^{2}+2)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2t^{2-1}$$

Subtract 1 from 2.

$$2t^{1}$$

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

$$2t$$

Differentiate w.r.t. t

$$2$$