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Popular >

derivative of sqrt(\sqrt{x+1)+1}

Solution

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

Solution

\frac{1}{4 x + 1 + 1 x + 1}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{2 x + 1 + 1} \cdot \frac{1}{2 x + 1}

Simplify

\frac{1}{2 x + 1 + 1} \cdot \frac{1}{2 x + 1} : \frac{1}{4 x + 1 + 1 x + 1}

= \frac{1}{4 x + 1 + 1 x + 1}

Popular Examples

tangent of f(x)=(5x)/(x^2+1),\at x=0 tangent of

f (x) = \frac{5 x}{x ^{2} + 1}, at x = 0

(dy)/(dθ)=sin^4(piθ)

\frac{d y}{d θ} = sin^{4} (π θ)

derivative of e^x+1/(e^x)

\frac{d}{d x} (e^{x} + \frac{1}{e ^{x}})

derivative of |x-1|

\frac{d}{d x} (∣ x - 1 ∣)

(4y+yx^2)dy-(2x+xy^2)dx=0

(4 y + y x^{2}) d y - (2 x + x y^{2}) d x = 0

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(\sqrt{x+1)+1} ?
The derivative of sqrt(\sqrt{x+1)+1} is 1/(4sqrt(\sqrt{x+1)+1)sqrt(x+1)}
What is the first derivative of sqrt(\sqrt{x+1)+1} ?
The first derivative of sqrt(\sqrt{x+1)+1} is 1/(4sqrt(\sqrt{x+1)+1)sqrt(x+1)}