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Popular Calculus >

derivative of y=x^{10}+1+sqrt(1-x)

Solution

derivative of

y = x^{10} + 1 + 1 - x

Solution

10 x^{9} - \frac{1}{2 - x + 1}

Solution steps

\frac{d}{d x} (x^{10} + 1 + 1 - x)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{10}) + \frac{d}{d x} (1) + \frac{d}{d x} (1 - x)

\frac{d}{d x} (x^{10}) = 10 x^{9}

\frac{d}{d x} (1) = 0

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

= 10 x^{9} + 0 - \frac{1}{2 1 - x}

Simplify

= 10 x^{9} - \frac{1}{2 - x + 1}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of y=x^{10}+1+sqrt(1-x) ?
The derivative of y=x^{10}+1+sqrt(1-x) is 10x^9-1/(2sqrt(-x+1))
What is the first derivative of y=x^{10}+1+sqrt(1-x) ?
The first derivative of y=x^{10}+1+sqrt(1-x) is 10x^9-1/(2sqrt(-x+1))