What is the derivative of f(x)=5sqrt(x)e^{x^2-3} ?

The derivative of f(x)=5sqrt(x)e^{x^2-3} is 5((e^{x^2-3})/(2sqrt(x))+2e^{x^2-3}xsqrt(x))

What is the first derivative of f(x)=5sqrt(x)e^{x^2-3} ?

The first derivative of f(x)=5sqrt(x)e^{x^2-3} is 5((e^{x^2-3})/(2sqrt(x))+2e^{x^2-3}xsqrt(x))

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derivative of

f (x) = 5 x e^{x^{2} - 3}

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{x^{2} - 3}

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

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} (e^{x^{2} - 3}) = e^{x^{2} - 3} \cdot 2 x

= 5 (\frac{1}{2 x} e^{x^{2} - 3} + e^{x^{2} - 3} \cdot 2 x x)

\frac{1}{2 x} e^{x^{2} - 3} = \frac{e ^{x^{2} - 3}}{2 x}

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

(5, 53)

(0, 3), (2, - 3)

y = 7

2 y^{2} - x = 14, (16, 3)

y = ln (\frac{1}{x x + 4})

What is the derivative of f(x)=5sqrt(x)e^{x^2-3} ?
The derivative of f(x)=5sqrt(x)e^{x^2-3} is 5((e^{x^2-3})/(2sqrt(x))+2e^{x^2-3}xsqrt(x))
What is the first derivative of f(x)=5sqrt(x)e^{x^2-3} ?
The first derivative of f(x)=5sqrt(x)e^{x^2-3} is 5((e^{x^2-3})/(2sqrt(x))+2e^{x^2-3}xsqrt(x))