What is the derivative of y=e^{sqrt(x)}(x^2-4) ?

The derivative of y=e^{sqrt(x)}(x^2-4) is (e^{sqrt(x)}(x^2-4))/(2sqrt(x))+2e^{sqrt(x)}x

What is the first derivative of y=e^{sqrt(x)}(x^2-4) ?

The first derivative of y=e^{sqrt(x)}(x^2-4) is (e^{sqrt(x)}(x^2-4))/(2sqrt(x))+2e^{sqrt(x)}x

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derivative of

y = e^{x} (x^{2} - 4)

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

Solution steps

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

Apply the Product Rule:

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

f = e^{x}, g = x^{2} - 4

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

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

\int y 10 + 8 y - 16 y^{2} d y

\frac{d}{d x} (sin (x) + 5)

(3, 4), (6, 8)

\int_{0}^{1} (x^{2} - x^{4}) d x

\frac{d}{d x} (\frac{3 x}{4 x ^{2} + 9})

What is the derivative of y=e^{sqrt(x)}(x^2-4) ?
The derivative of y=e^{sqrt(x)}(x^2-4) is (e^{sqrt(x)}(x^2-4))/(2sqrt(x))+2e^{sqrt(x)}x
What is the first derivative of y=e^{sqrt(x)}(x^2-4) ?
The first derivative of y=e^{sqrt(x)}(x^2-4) is (e^{sqrt(x)}(x^2-4))/(2sqrt(x))+2e^{sqrt(x)}x