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Popular >

derivative of e^x(1-y^2)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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Frequently Asked Questions (FAQ)

What is the derivative of e^x(1-y^2) ?
The derivative of e^x(1-y^2) is e^x(1-y)^2-2e^x(1-y)(dy)/(dx)
What is the first derivative of e^x(1-y^2) ?
The first derivative of e^x(1-y^2) is e^x(1-y)^2-2e^x(1-y)(dy)/(dx)