What is the derivative of f(x)=(x^2-1)(1-e^x) ?

The derivative of f(x)=(x^2-1)(1-e^x) is 2x(1-e^x)-e^x(x^2-1)

What is the first derivative of f(x)=(x^2-1)(1-e^x) ?

The first derivative of f(x)=(x^2-1)(1-e^x) is 2x(1-e^x)-e^x(x^2-1)

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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\frac{\partial}{\partial y} (x^{2} y^{2} z)

y^{^{'}} + 6 y = t + e^{- 5 t}

What is the derivative of f(x)=(x^2-1)(1-e^x) ?
The derivative of f(x)=(x^2-1)(1-e^x) is 2x(1-e^x)-e^x(x^2-1)
What is the first derivative of f(x)=(x^2-1)(1-e^x) ?
The first derivative of f(x)=(x^2-1)(1-e^x) is 2x(1-e^x)-e^x(x^2-1)