Solve 2e^|x-x+c

$$2 e ^ { | x - x } + c$$

Evaluate

$$2\left(c+1\right)$$

Solution Steps

Combine x and -x to get 0.

$$2\left(e^{|0|}+c\right)$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 0 is 0.

$$2\left(e^{0}+c\right)$$

Calculate e to the power of 0 and get 1.

$$2\left(1+c\right)$$

Use the distributive property to multiply 2 by 1+c.

$$2+2c$$

Differentiate w.r.t. c

$$2$$

Steps Using Derivative Rule for Sum

Combine x and -x to get 0.

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

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 0 is 0.

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

Calculate e to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}c}(2\left(1+c\right))$$

Use the distributive property to multiply 2 by 1+c.

$$\frac{\mathrm{d}}{\mathrm{d}c}(2+2c)$$

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}.

$$2c^{1-1}$$

Subtract 1 from 1.

$$2c^{0}$$

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

$$2\times 1$$

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

$$2$$