What is the derivative of arctan(x^4y^3) ?

The derivative of arctan(x^4y^3) is (4x^3y^3+3x^4y^2\frac{dy)/(dx)}{x^8y^6+1}

What is the first derivative of arctan(x^4y^3) ?

The first derivative of arctan(x^4y^3) is (4x^3y^3+3x^4y^2\frac{dy)/(dx)}{x^8y^6+1}

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\frac{d}{d x} (arctan (x^{4} y^{3}))

\frac{4 x ^{3} y ^{3} + 3 x ^{4} y ^{2} \frac{d y}{d x}}{x ^{8} y ^{6} + 1}

Solution steps

\frac{d}{d x} (arctan (x^{4} y^{3}))

Apply the chain rule:

\frac{1}{( x ^{4} y ^{3} ) ^{2} + 1} \frac{d}{d x} (x^{4} y^{3})

= \frac{1}{( x ^{4} y ^{3} ) ^{2} + 1} \frac{d}{d x} (x^{4} y^{3})

\frac{d}{d x} (x^{4} y^{3}) = 4 x^{3} y^{3} + 3 y^{2} \frac{d y}{d x} x^{4}

= \frac{1}{( x ^{4} y ^{3} ) ^{2} + 1} (4 x^{3} y^{3} + 3 y^{2} \frac{d y}{d x} x^{4})

Simplify

\frac{1}{( x ^{4} y ^{3} ) ^{2} + 1} (4 x^{3} y^{3} + 3 y^{2} \frac{d y}{d x} x^{4}) : \frac{4 x ^{3} y ^{3} + 3 x ^{4} y ^{2} \frac{d y}{d x}}{x ^{8} y ^{6} + 1}

= \frac{4 x ^{3} y ^{3} + 3 x ^{4} y ^{2} \frac{d y}{d x}}{x ^{8} y ^{6} + 1}

\int \frac{x + 3}{x + 6} d x

x \to 0 + lim (\frac{2}{1 + ln ( x )})

f (x) = x, at x = 2

\frac{d y}{d t} + e^{t} y = - 3 e^{t}

What is the derivative of arctan(x^4y^3) ?
The derivative of arctan(x^4y^3) is (4x^3y^3+3x^4y^2\frac{dy)/(dx)}{x^8y^6+1}
What is the first derivative of arctan(x^4y^3) ?
The first derivative of arctan(x^4y^3) is (4x^3y^3+3x^4y^2\frac{dy)/(dx)}{x^8y^6+1}