What is the derivative of e^{1-x}*(5-x^2) ?

The derivative of e^{1-x}*(5-x^2) is -e^{1-x}(5-x^2)-2e^{1-x}x

What is the first derivative of e^{1-x}*(5-x^2) ?

The first derivative of e^{1-x}*(5-x^2) is -e^{1-x}(5-x^2)-2e^{1-x}x

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derivative of

e^{1 - x} \cdot (5 - x^{2})

- e^{1 - x} (5 - x^{2}) - 2 e^{1 - x} x

Solution steps

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

Apply the Product Rule:

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

f = e^{1 - x}, g = 5 - x^{2}

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

\frac{d}{d x} (e^{1 - x}) = - e^{1 - x}

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

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

Simplify

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

f (x) = (7 x^{4} - 6 x^{3} - 5 x)^{8}

\int 120 x \cdot (2 x + 1)^{4} d x

\int \frac{1}{3} e^{- \frac{x}{2}} (x + 1) d x

\int sec^{8} (t) an x d x

\int - \frac{1}{9} x^{- \frac{10}{9}} d x

What is the derivative of e^{1-x}*(5-x^2) ?
The derivative of e^{1-x}*(5-x^2) is -e^{1-x}(5-x^2)-2e^{1-x}x
What is the first derivative of e^{1-x}*(5-x^2) ?
The first derivative of e^{1-x}*(5-x^2) is -e^{1-x}(5-x^2)-2e^{1-x}x