What is the derivative of y=(x^2+e^x)sqrt(x) ?

The derivative of y=(x^2+e^x)sqrt(x) is (5x^2+2e^xx+e^x)/(2sqrt(x))

What is the first derivative of y=(x^2+e^x)sqrt(x) ?

The first derivative of y=(x^2+e^x)sqrt(x) is (5x^2+2e^xx+e^x)/(2sqrt(x))

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derivative of

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

\frac{5 x ^{2} + 2 e ^{x} x + e ^{x}}{2 x}

Solution steps

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

Apply the Product Rule:

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

f = x^{2} + e^{x}, g = x

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

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

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

= (2 x + e^{x}) x + \frac{1}{2 x} (x^{2} + e^{x})

Simplify

(2 x + e^{x}) x + \frac{1}{2 x} (x^{2} + e^{x}) : \frac{5 x ^{2} + 2 e ^{x} x + e ^{x}}{2 x}

= \frac{5 x ^{2} + 2 e ^{x} x + e ^{x}}{2 x}

\frac{d}{d y} (x sin (y))

x \to \infty lim (\frac{5}{4})

\frac{d}{d x} (I n e^{x})

\int (x^{17} + 3 e^{x} - cos (x) + \frac{1}{x}) d x

f (x) = x^{- 6}

What is the derivative of y=(x^2+e^x)sqrt(x) ?
The derivative of y=(x^2+e^x)sqrt(x) is (5x^2+2e^xx+e^x)/(2sqrt(x))
What is the first derivative of y=(x^2+e^x)sqrt(x) ?
The first derivative of y=(x^2+e^x)sqrt(x) is (5x^2+2e^xx+e^x)/(2sqrt(x))