Solve (x+1)*e^-05x

$$( x + 1 ) \cdot e ^ { - 05 x }$$

Evaluate

$$x+1$$

Solution Steps

Multiply 0 and 5 to get 0.

$$\left(x+1\right)e^{0x}$$

Anything times zero gives zero.

$$\left(x+1\right)e^{0}$$

Calculate e to the power of 0 and get 1.

$$\left(x+1\right)\times 1$$

Use the distributive property to multiply x+1 by 1.

$$x+1$$

Differentiate w.r.t. x

$$1$$

Steps Using Derivative Rule for Sum

Multiply 0 and 5 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(x+1\right)e^{0x})$$

Anything times zero gives zero.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(x+1\right)e^{0})$$

Calculate e to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(x+1\right)\times 1)$$

Use the distributive property to multiply x+1 by 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x+1)$$

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}.

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

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

$$1$$