What is the derivative of-2arcsec(x+1) ?

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

What is the first derivative of-2arcsec(x+1) ?

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

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

- \frac{2}{( x + 1 ) x ^{2} + 2 x}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int sin (a \cdot x) cos (a \cdot x) d x

\int 8 e^{- x} d x

\frac{d y}{d x} = \frac{k}{x}

\frac{\partial}{\partial x} (10 e^{x^{7} y})

1.8 e^{2 x} - 45

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