What is the derivative of arcsin(x^3y) ?

The derivative of arcsin(x^3y) is (3x^2y+x^3\frac{dy)/(dx)}{sqrt(1-x^6y^2)}

What is the first derivative of arcsin(x^3y) ?

The first derivative of arcsin(x^3y) is (3x^2y+x^3\frac{dy)/(dx)}{sqrt(1-x^6y^2)}

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\frac{d}{d x} (arcsin (x^{3} y))

\frac{3 x ^{2} y + x ^{3} \frac{d y}{d x}}{1 - x ^{6} y ^{2}}

Solution steps

\frac{d}{d x} (arcsin (x^{3} y))

Apply the chain rule:

\frac{1}{1 - ( x ^{3} y ) ^{2}} \frac{d}{d x} (x^{3} y)

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

\frac{d}{d x} (x^{3} y) = 3 x^{2} y + \frac{d y}{d x} x^{3}

= \frac{1}{1 - ( x ^{3} y ) ^{2}} (3 x^{2} y + \frac{d y}{d x} x^{3})

Simplify

\frac{1}{1 - ( x ^{3} y ) ^{2}} (3 x^{2} y + \frac{d y}{d x} x^{3}) : \frac{3 x ^{2} y + x ^{3} \frac{d y}{d x}}{1 - x ^{6} y ^{2}}

= \frac{3 x ^{2} y + x ^{3} \frac{d y}{d x}}{1 - x ^{6} y ^{2}}

\int e^{2 x} d x

\int_{1}^{e^{2}} \frac{3}{x} d x

\int \frac{1}{( 2 x + 5 ) ^{2}} d x

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

\int \frac{x ^{4} + x - 36}{x ^{2} + 6} d x

What is the derivative of arcsin(x^3y) ?
The derivative of arcsin(x^3y) is (3x^2y+x^3\frac{dy)/(dx)}{sqrt(1-x^6y^2)}
What is the first derivative of arcsin(x^3y) ?
The first derivative of arcsin(x^3y) is (3x^2y+x^3\frac{dy)/(dx)}{sqrt(1-x^6y^2)}