What is the derivative of sqrt(4x^2+1) ?

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (4 x^{2} + 1) = 8 x

= \frac{1}{2 4 x ^{2} + 1} \cdot 8 x

Simplify

\frac{1}{2 4 x ^{2} + 1} \cdot 8 x : \frac{4 x}{4 x ^{2} + 1}

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

\frac{d}{d x} (sin (4 x + 1))

cos (t) + t sin (t), at t = 0

\frac{d y}{d x} = \frac{x ^{2} + y ^{2} - x y}{x ^{2}}

\int ln (a x) d x

\int \frac{18}{( 81 x ^{2} + 1 ) ^{2}} d x

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