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Popular >

derivative of 9xe^{-x}

Solution

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

Solution

9 (e^{- x} - e^{- x} x)

Solution steps

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

Take the constant out:

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

= 9 \frac{d}{d x} (x e^{- x})

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

= 9 (1 \cdot e^{- x} + (- e^{- x}) x)

Simplify

= 9 (e^{- x} - e^{- x} x)

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\int cos (z)

(1+x^2)y^{''}-2xy^'+2y=0

(1 + x^{2}) y^{^{''}} - 2 x y^{^{'}} + 2 y = 0

(d^3)/(dx^3)(ln(x+2))

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

derivative of f(t)=sqrt(9t^2-t)derivative of

f (t) = 9 t^{2} - t

Frequently Asked Questions (FAQ)

What is the derivative of 9xe^{-x} ?
The derivative of 9xe^{-x} is 9(e^{-x}-e^{-x}x)
What is the first derivative of 9xe^{-x} ?
The first derivative of 9xe^{-x} is 9(e^{-x}-e^{-x}x)