What is the derivative of 5xarcsin(x) ?

The derivative of 5xarcsin(x) is 5(arcsin(x)+x/(sqrt(1-x^2)))

What is the first derivative of 5xarcsin(x) ?

The first derivative of 5xarcsin(x) is 5(arcsin(x)+x/(sqrt(1-x^2)))

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derivative of

5 x arcsin (x)

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

Solution steps

\frac{d}{d x} (5 x arcsin (x))

Take the constant out:

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

= 5 \frac{d}{d x} (x arcsin (x))

Apply the Product Rule:

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

f = x, g = arcsin (x)

= 5 (\frac{d x}{d x} arcsin (x) + \frac{d}{d x} (arcsin (x)) x)

\frac{d x}{d x} = 1

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

= 5 (1 \cdot arcsin (x) + \frac{1}{1 - x ^{2}} x)

Simplify

5 (1 \cdot arcsin (x) + \frac{1}{1 - x ^{2}} x) : 5 (arcsin (x) + \frac{x}{1 - x ^{2}})

= 5 (arcsin (x) + \frac{x}{1 - x ^{2}})

\int \frac{1 - 2 y}{y ^{2}} d y

\frac{d}{d x} (e^{x + y} - x)

\frac{d}{d x} (cos (sin (6 x)))

\frac{\partial}{\partial y} (\frac{1 + t ^{2}}{3 y - y ^{2}})

\frac{4 x ^{2} + 6 x + 6}{x}

What is the derivative of 5xarcsin(x) ?
The derivative of 5xarcsin(x) is 5(arcsin(x)+x/(sqrt(1-x^2)))
What is the first derivative of 5xarcsin(x) ?
The first derivative of 5xarcsin(x) is 5(arcsin(x)+x/(sqrt(1-x^2)))