What is the derivative of f(x)=sqrt(x^3+x^2+x+1) ?

The derivative of f(x)=sqrt(x^3+x^2+x+1) is (3x^2+2x+1)/(2sqrt(x^3+x^2+x+1))

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

The first derivative of f(x)=sqrt(x^3+x^2+x+1) is (3x^2+2x+1)/(2sqrt(x^3+x^2+x+1))

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derivative of

f (x) = x^{3} + x^{2} + x + 1

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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