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Popular >

derivative of f(t)=sqrt(t+\sqrt{t)}

Solution

derivative of

f (t) = t + t

Solution

\frac{2 t + 1}{4 t t + t}

Solution steps

\frac{d}{d t} (t + t)

Apply the chain rule:

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

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

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

= \frac{1}{2 t + t} (1 + \frac{1}{2 t})

Simplify

\frac{1}{2 t + t} (1 + \frac{1}{2 t}) : \frac{2 t + 1}{4 t t + t}

= \frac{2 t + 1}{4 t t + t}

Popular Examples

integral of 3/(x+2)

\int \frac{3}{x + 2} d x

integral from 1 to 3 of sqrt(1+4x^2)

\int_{1}^{3} 1 + 4 x^{2} d x

(\partial)/(\partial x)(2x-2)

\frac{\partial}{\partial x} (2 x - 2)

limit as t approaches 0 of 3/t-3/(t^2+t)

t \to 0 lim (\frac{3}{t} - \frac{3}{t ^{2} + t})

integral of 4/(x^5)-3/(x^4)

\int \frac{4}{x ^{5}} - \frac{3}{x ^{4}} d x

Frequently Asked Questions (FAQ)

What is the derivative of f(t)=sqrt(t+\sqrt{t)} ?
The derivative of f(t)=sqrt(t+\sqrt{t)} is (2sqrt(t)+1)/(4sqrt(t)\sqrt{t+\sqrt{t)}}
What is the first derivative of f(t)=sqrt(t+\sqrt{t)} ?
The first derivative of f(t)=sqrt(t+\sqrt{t)} is (2sqrt(t)+1)/(4sqrt(t)\sqrt{t+\sqrt{t)}}