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Popular Calculus >

derivative of p(x)=sqrt(x)-sqrt(1-3x^2)

Solution

derivative of

p (x) = x - 1 - 3 x^{2}

Solution

\frac{1}{2 x} + \frac{3 x}{1 - 3 x ^{2}}

Solution steps

\frac{d}{d x} (x - 1 - 3 x^{2})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x) - \frac{d}{d x} (1 - 3 x^{2})

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

\frac{d}{d x} (1 - 3 x^{2}) = - \frac{3 x}{1 - 3 x ^{2}}

= \frac{1}{2 x} - (- \frac{3 x}{1 - 3 x ^{2}})

Simplify

= \frac{1}{2 x} + \frac{3 x}{1 - 3 x ^{2}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of p(x)=sqrt(x)-sqrt(1-3x^2) ?
The derivative of p(x)=sqrt(x)-sqrt(1-3x^2) is 1/(2sqrt(x))+(3x)/(sqrt(1-3x^2))
What is the first derivative of p(x)=sqrt(x)-sqrt(1-3x^2) ?
The first derivative of p(x)=sqrt(x)-sqrt(1-3x^2) is 1/(2sqrt(x))+(3x)/(sqrt(1-3x^2))