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Popular >

derivative of g(x)=sqrt(x+x^3)

Solution

derivative of

g (x) = x + x^{3}

Solution

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

Solution steps

\frac{d}{d x} (x + x^{3})

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 x + x ^{3}} (1 + 3 x^{2}) : \frac{1 + 3 x ^{2}}{2 x + x ^{3}}

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

Popular Examples

integral of (1+cos(2x))/2

\int \frac{1 + cos ( 2 x )}{2} d x

f(x)=(sec(x)+tan(x))/(sec(x)-tan(x))

f (x) = \frac{sec ( x ) + tan ( x )}{sec ( x ) - tan ( x )}

derivative of (4x/((x+1)))

\frac{d}{d x} (\frac{4 x}{( x + 1 )})

integral of 1/(4+3x^2)

\int \frac{1}{4 + 3 x ^{2}} d x

integral of (x+4)cos(n)pix

\int (x + 4) cos (n) π x d x

Frequently Asked Questions (FAQ)

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