What is the derivative of x^2arcsinh(9x) ?

The derivative of x^2arcsinh(9x) is 2xarcsinh(9x)+(9x^2)/(sqrt(81x^2+1))

What is the first derivative of x^2arcsinh(9x) ?

The first derivative of x^2arcsinh(9x) is 2xarcsinh(9x)+(9x^2)/(sqrt(81x^2+1))

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\frac{d}{d x} (x^{2} arcsinh (9 x))

2 x arcsinh (9 x) + \frac{9 x ^{2}}{81 x ^{2} + 1}

Solution steps

\frac{d}{d x} (x^{2} arcsinh (9 x))

Apply the Product Rule:

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

f = x^{2}, g = arcsinh (9 x)

= \frac{d}{d x} (x^{2}) arcsinh (9 x) + \frac{d}{d x} (arcsinh (9 x)) x^{2}

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (arcsinh (9 x)) = \frac{9}{81 x ^{2} + 1}

= 2 x arcsinh (9 x) + \frac{9}{81 x ^{2} + 1} x^{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 2 x arcsinh (9 x) + \frac{9 x ^{2}}{81 x ^{2} + 1}

\int \frac{1}{x ^{5}} - \frac{3}{x ^{2}} d x

x y^{^{'}} + 2 y = x^{2} - x + 1

f (x) = ln (x^{2} - 9 x + 1), (9, 0)

(- 2, 2), (1, - 2)

6 t^{2}

What is the derivative of x^2arcsinh(9x) ?
The derivative of x^2arcsinh(9x) is 2xarcsinh(9x)+(9x^2)/(sqrt(81x^2+1))
What is the first derivative of x^2arcsinh(9x) ?
The first derivative of x^2arcsinh(9x) is 2xarcsinh(9x)+(9x^2)/(sqrt(81x^2+1))