What is the derivative of 2e^x+3x^2+x^{3/2}+5 ?

The derivative of 2e^x+3x^2+x^{3/2}+5 is 6x+(3x^{1/2})/2+2e^x

What is the first derivative of 2e^x+3x^2+x^{3/2}+5 ?

The first derivative of 2e^x+3x^2+x^{3/2}+5 is 6x+(3x^{1/2})/2+2e^x

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

6 x + \frac{3 x ^{\frac{1}{2}}}{2} + 2 e^{x}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (3 x^{2}) = 6 x

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

\frac{d}{d x} (5) = 0

= 2 e^{x} + 6 x + \frac{3 x ^{\frac{1}{2}}}{2} + 0

Simplify

= 6 x + \frac{3 x ^{\frac{1}{2}}}{2} + 2 e^{x}

x \to 0 lim (\frac{5 x + 1}{x})

\frac{2 s + 5}{s ^{2} - s - 6}

x \to 0 lim ((1 + \frac{3}{x ^{5}})^{x})

\frac{d}{d x} (6 e^{- x})

y = 5 x, y = \frac{1}{7} x, y = 50 - x^{2}

What is the derivative of 2e^x+3x^2+x^{3/2}+5 ?
The derivative of 2e^x+3x^2+x^{3/2}+5 is 6x+(3x^{1/2})/2+2e^x
What is the first derivative of 2e^x+3x^2+x^{3/2}+5 ?
The first derivative of 2e^x+3x^2+x^{3/2}+5 is 6x+(3x^{1/2})/2+2e^x