What is the derivative of y=(3-e^x)^3 ?

The derivative of y=(3-e^x)^3 is -3e^x(3-e^x)^2

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

The first derivative of y=(3-e^x)^3 is -3e^x(3-e^x)^2

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derivative of

y = (3 - e^{x})^{3}

- 3 e^{x} (3 - e^{x})^{2}

Solution steps

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

Apply the chain rule:

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

= 3 (3 - e^{x})^{2} \frac{d}{d x} (3 - e^{x})

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

= 3 (3 - e^{x})^{2} (- e^{x})

Simplify

= - 3 e^{x} (3 - e^{x})^{2}

What is the derivative of y=(3-e^x)^3 ?
The derivative of y=(3-e^x)^3 is -3e^x(3-e^x)^2
What is the first derivative of y=(3-e^x)^3 ?
The first derivative of y=(3-e^x)^3 is -3e^x(3-e^x)^2