What is the derivative of y=(1-e^x)^4 ?

The derivative of y=(1-e^x)^4 is -4e^x(1-e^x)^3

What is the first derivative of y=(1-e^x)^4 ?

The first derivative of y=(1-e^x)^4 is -4e^x(1-e^x)^3

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derivative of

y = (1 - e^{x})^{4}

- 4 e^{x} (1 - e^{x})^{3}

Solution steps

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

Apply the chain rule:

4 (1 - e^{x})^{3} \frac{d}{d x} (1 - e^{x})

= 4 (1 - e^{x})^{3} \frac{d}{d x} (1 - e^{x})

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

= 4 (1 - e^{x})^{3} (- e^{x})

Simplify

= - 4 e^{x} (1 - e^{x})^{3}

\frac{\partial}{\partial x} (\frac{1}{2} m v^{2})

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500 (3 + \frac{5 t}{30 + t ^{2}})

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\frac{\partial}{\partial y} (x^{3} + x^{2} y^{3} - 2 y^{2})

What is the derivative of y=(1-e^x)^4 ?
The derivative of y=(1-e^x)^4 is -4e^x(1-e^x)^3
What is the first derivative of y=(1-e^x)^4 ?
The first derivative of y=(1-e^x)^4 is -4e^x(1-e^x)^3