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Popular >

derivative of 5e^{-x}-3e^{-5x}

Solution

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

Solution

- 5 e^{- x} + 15 e^{- 5 x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (3 e^{- 5 x}) = - 15 e^{- 5 x}

= - 5 e^{- x} - (- 15 e^{- 5 x})

Simplify

= - 5 e^{- x} + 15 e^{- 5 x}

Popular Examples

derivative of f(x)=(x^2+1)*e^{x-1}derivative of

f (x) = (x^{2} + 1) \cdot e^{x - 1}

81y^{''}+72y^'+16y=0,y^'(0)=-1

81 y^{^{''}} + 72 y^{^{'}} + 16 y = 0, y^{^{'}} (0) = - 1

derivative of x^{9/4}+e^{-2x}

\frac{d}{d x} (x^{\frac{9}{4}} + e^{- 2 x})

2(dy)/(dx)+6y+4=0

2 \frac{d y}{d x} + 6 y + 4 = 0

derivative of f(x)=(3x^2+3x-1)^4 derivative of

f (x) = (3 x^{2} + 3 x - 1)^{4}

Frequently Asked Questions (FAQ)

What is the derivative of 5e^{-x}-3e^{-5x} ?
The derivative of 5e^{-x}-3e^{-5x} is -5e^{-x}+15e^{-5x}
What is the first derivative of 5e^{-x}-3e^{-5x} ?
The first derivative of 5e^{-x}-3e^{-5x} is -5e^{-x}+15e^{-5x}