What is the derivative of e^{x^2-4}+3x+5 ?

The derivative of e^{x^2-4}+3x+5 is 2e^{x^2-4}x+3

What is the first derivative of e^{x^2-4}+3x+5 ?

The first derivative of e^{x^2-4}+3x+5 is 2e^{x^2-4}x+3

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\frac{d}{d x} (e^{x^{2} - 4} + 3 x + 5)

2 e^{x^{2} - 4} x + 3

Solution steps

\frac{d}{d x} (e^{x^{2} - 4} + 3 x + 5)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (e^{x^{2} - 4}) + \frac{d}{d x} (3 x) + \frac{d}{d x} (5)

\frac{d}{d x} (e^{x^{2} - 4}) = e^{x^{2} - 4} \cdot 2 x

\frac{d}{d x} (3 x) = 3

\frac{d}{d x} (5) = 0

= e^{x^{2} - 4} \cdot 2 x + 3 + 0

Simplify

= 2 e^{x^{2} - 4} x + 3

What is the derivative of e^{x^2-4}+3x+5 ?
The derivative of e^{x^2-4}+3x+5 is 2e^{x^2-4}x+3
What is the first derivative of e^{x^2-4}+3x+5 ?
The first derivative of e^{x^2-4}+3x+5 is 2e^{x^2-4}x+3