What is the derivative of (x+e^x(3-sqrt(x))) ?

The derivative of (x+e^x(3-sqrt(x))) is (-3x-2e^xx+6e^xsqrt(x)-e^x)/(2sqrt(x))+3

What is the first derivative of (x+e^x(3-sqrt(x))) ?

The first derivative of (x+e^x(3-sqrt(x))) is (-3x-2e^xx+6e^xsqrt(x)-e^x)/(2sqrt(x))+3

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

\frac{- 3 x - 2 e ^{x} x + 6 e ^{x} x - e ^{x}}{2 x} + 3

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (3 - x) = - \frac{1}{2 x}

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

Simplify

(1 + e^{x}) (3 - x) + (- \frac{1}{2 x}) (x + e^{x}) : \frac{- 3 x - 2 e ^{x} x + 6 e ^{x} x - e ^{x}}{2 x} + 3

= \frac{- 3 x - 2 e ^{x} x + 6 e ^{x} x - e ^{x}}{2 x} + 3

What is the derivative of (x+e^x(3-sqrt(x))) ?
The derivative of (x+e^x(3-sqrt(x))) is (-3x-2e^xx+6e^xsqrt(x)-e^x)/(2sqrt(x))+3
What is the first derivative of (x+e^x(3-sqrt(x))) ?
The first derivative of (x+e^x(3-sqrt(x))) is (-3x-2e^xx+6e^xsqrt(x)-e^x)/(2sqrt(x))+3