What is the derivative of f(x)=e^{x^2+5x} ?

The derivative of f(x)=e^{x^2+5x} is e^{x^2+5x}(2x+5)

What is the first derivative of f(x)=e^{x^2+5x} ?

The first derivative of f(x)=e^{x^2+5x} is e^{x^2+5x}(2x+5)

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derivative

e^{x^{2} + 5 x} (2 x + 5)

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{2} + 5 x) = 2 x + 5

= e^{x^{2} + 5 x} (2 x + 5)

What is the derivative of f(x)=e^{x^2+5x} ?
The derivative of f(x)=e^{x^2+5x} is e^{x^2+5x}(2x+5)
What is the first derivative of f(x)=e^{x^2+5x} ?
The first derivative of f(x)=e^{x^2+5x} is e^{x^2+5x}(2x+5)