What is the derivative of arcsin(3xln(sqrt(x+1))) ?

The derivative of arcsin(3xln(sqrt(x+1))) is (3ln(x+1))/(2sqrt(1-9x^2))+(arcsin(3x))/(2(x+1))

What is the first derivative of arcsin(3xln(sqrt(x+1))) ?

The first derivative of arcsin(3xln(sqrt(x+1))) is (3ln(x+1))/(2sqrt(1-9x^2))+(arcsin(3x))/(2(x+1))

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\frac{d}{d x} (arcsin (3 x) ln (x + 1))

\frac{3 ln ( x + 1 )}{2 1 - 9 x ^{2}} + \frac{arcsin ( 3 x )}{2 ( x + 1 )}

Solution steps

\frac{d}{d x} (arcsin (3 x) ln (x + 1))

Apply the Product Rule:

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

f = arcsin (3 x), g = ln (x + 1)

= \frac{d}{d x} (arcsin (3 x)) ln (x + 1) + \frac{d}{d x} (ln (x + 1)) arcsin (3 x)

\frac{d}{d x} (arcsin (3 x)) = \frac{3}{1 - 9 x ^{2}}

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

= \frac{3}{1 - 9 x ^{2}} ln (x + 1) + \frac{1}{2 ( x + 1 )} arcsin (3 x)

Simplify

\frac{3}{1 - 9 x ^{2}} ln (x + 1) + \frac{1}{2 ( x + 1 )} arcsin (3 x) : \frac{3 ln ( x + 1 )}{2 1 - 9 x ^{2}} + \frac{arcsin ( 3 x )}{2 ( x + 1 )}

= \frac{3 ln ( x + 1 )}{2 1 - 9 x ^{2}} + \frac{arcsin ( 3 x )}{2 ( x + 1 )}

\int 3 x zy + x y^{2} + 2 z x^{2}

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

\int \frac{( x ^{2} + 4 )}{( x - 5 ) ( x ^{2} + 9 )} d x

\int x^{4} e^{(1 - x^{5})} d x

\frac{d y}{d x} + 5 y = 8

What is the derivative of arcsin(3xln(sqrt(x+1))) ?
The derivative of arcsin(3xln(sqrt(x+1))) is (3ln(x+1))/(2sqrt(1-9x^2))+(arcsin(3x))/(2(x+1))
What is the first derivative of arcsin(3xln(sqrt(x+1))) ?
The first derivative of arcsin(3xln(sqrt(x+1))) is (3ln(x+1))/(2sqrt(1-9x^2))+(arcsin(3x))/(2(x+1))