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Popular >

derivative of f(x)=(4e^x+5e^{-x})/6

Solution

derivative of

f (x) = \frac{4 e ^{x} + 5 e ^{- x}}{6}

Solution

\frac{1}{6} (4 e^{x} - 5 e^{- x})

Solution steps

\frac{d}{d x} (\frac{4 e ^{x} + 5 e ^{- x}}{6})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{6} \frac{d}{d x} (4 e^{x} + 5 e^{- x})

Apply the Sum/Difference Rule:

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

= \frac{1}{6} (\frac{d}{d x} (4 e^{x}) + \frac{d}{d x} (5 e^{- x}))

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

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

= \frac{1}{6} (4 e^{x} - 5 e^{- x})

Popular Examples

(\partial)/(\partial x)(1/(x^2+4))

\frac{\partial}{\partial x} (\frac{1}{x ^{2} + 4})

(dy)/(dx)=(x^3)/(y+1)

\frac{d y}{d x} = \frac{x ^{3}}{y + 1}

xy^'-y=sqrt(x^2+y^2)

x y^{^{'}} - y = x^{2} + y^{2}

limit as x approaches 2 of 5x^3-3x^2+x-6

x \to 2 lim (5 x^{3} - 3 x^{2} + x - 6)

area e^x,xe^x,x=0 area

e^{x}, x e^{x}, x = 0

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(4e^x+5e^{-x})/6 ?
The derivative of f(x)=(4e^x+5e^{-x})/6 is 1/6 (4e^x-5e^{-x})
What is the first derivative of f(x)=(4e^x+5e^{-x})/6 ?
The first derivative of f(x)=(4e^x+5e^{-x})/6 is 1/6 (4e^x-5e^{-x})