What is the derivative of f(x)=sqrt(x^4+x^2+2) ?

The derivative of f(x)=sqrt(x^4+x^2+2) is (x(2x^2+1))/(sqrt(x^4+x^2+2))

What is the first derivative of f(x)=sqrt(x^4+x^2+2) ?

The first derivative of f(x)=sqrt(x^4+x^2+2) is (x(2x^2+1))/(sqrt(x^4+x^2+2))

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derivative of

f (x) = x^{4} + x^{2} + 2

\frac{x ( 2 x ^{2} + 1 )}{x ^{4} + x ^{2} + 2}

Solution steps

\frac{d}{d x} (x^{4} + x^{2} + 2)

Apply the chain rule:

\frac{1}{2 x ^{4} + x ^{2} + 2} \frac{d}{d x} (x^{4} + x^{2} + 2)

= \frac{1}{2 x ^{4} + x ^{2} + 2} \frac{d}{d x} (x^{4} + x^{2} + 2)

\frac{d}{d x} (x^{4} + x^{2} + 2) = 4 x^{3} + 2 x

= \frac{1}{2 x ^{4} + x ^{2} + 2} (4 x^{3} + 2 x)

Simplify

\frac{1}{2 x ^{4} + x ^{2} + 2} (4 x^{3} + 2 x) : \frac{x ( 2 x ^{2} + 1 )}{x ^{4} + x ^{2} + 2}

= \frac{x ( 2 x ^{2} + 1 )}{x ^{4} + x ^{2} + 2}

x \to 4 lim (\frac{a x ^{4}}{x - 4})

\int e^{5 x} x d x

f (x) = e^{- x + 1} - e^{- x + 1} x

\int \frac{1}{z} - \frac{x}{y ^{2}} d y

\int_{- 1}^{1} e^{x} - x^{2} - 1 d x

What is the derivative of f(x)=sqrt(x^4+x^2+2) ?
The derivative of f(x)=sqrt(x^4+x^2+2) is (x(2x^2+1))/(sqrt(x^4+x^2+2))
What is the first derivative of f(x)=sqrt(x^4+x^2+2) ?
The first derivative of f(x)=sqrt(x^4+x^2+2) is (x(2x^2+1))/(sqrt(x^4+x^2+2))