What is the derivative of sqrt(r)(2r+1) ?

The derivative of sqrt(r)(2r+1) is (6r+1)/(2sqrt(r))

What is the first derivative of sqrt(r)(2r+1) ?

The first derivative of sqrt(r)(2r+1) is (6r+1)/(2sqrt(r))

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derivative of

r (2 r + 1)

\frac{6 r + 1}{2 r}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = r, g = 2 r + 1

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

\frac{d}{d r} (r) = \frac{1}{2 r}

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

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

Simplify

\frac{1}{2 r} (2 r + 1) + 2 r : \frac{6 r + 1}{2 r}

= \frac{6 r + 1}{2 r}

\frac{d y}{d t} = 5 (y - t^{2})

\int \frac{x ^{3}}{( 2 + x ^{4} ) ^{9}} d x

y^{^{'}} = 2 y - 3 e^{- t}

x \to 0 lim (sin (\frac{2}{x}))

f (x) = 2 x + x

What is the derivative of sqrt(r)(2r+1) ?
The derivative of sqrt(r)(2r+1) is (6r+1)/(2sqrt(r))
What is the first derivative of sqrt(r)(2r+1) ?
The first derivative of sqrt(r)(2r+1) is (6r+1)/(2sqrt(r))