What is the derivative of (5x+e^x(5-sqrt(x))) ?

The derivative of (5x+e^x(5-sqrt(x))) is (-15x-2e^xx+10e^xsqrt(x)-e^x)/(2sqrt(x))+25

What is the first derivative of (5x+e^x(5-sqrt(x))) ?

The first derivative of (5x+e^x(5-sqrt(x))) is (-15x-2e^xx+10e^xsqrt(x)-e^x)/(2sqrt(x))+25

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

\frac{- 15 x - 2 e ^{x} x + 10 e ^{x} x - e ^{x}}{2 x} + 25

Solution steps

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

Apply the Product Rule:

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

f = 5 x + e^{x}, g = 5 - x

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

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

\frac{d}{d x} (5 - x) = - \frac{1}{2 x}

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

Simplify

(5 + e^{x}) (5 - x) + (- \frac{1}{2 x}) (5 x + e^{x}) : \frac{- 15 x - 2 e ^{x} x + 10 e ^{x} x - e ^{x}}{2 x} + 25

= \frac{- 15 x - 2 e ^{x} x + 10 e ^{x} x - e ^{x}}{2 x} + 25

What is the derivative of (5x+e^x(5-sqrt(x))) ?
The derivative of (5x+e^x(5-sqrt(x))) is (-15x-2e^xx+10e^xsqrt(x)-e^x)/(2sqrt(x))+25
What is the first derivative of (5x+e^x(5-sqrt(x))) ?
The first derivative of (5x+e^x(5-sqrt(x))) is (-15x-2e^xx+10e^xsqrt(x)-e^x)/(2sqrt(x))+25