Final answer to the problem
$4\left(\frac{1}{1+16x^{4}y^2}\right)x\left(2y+xy^{\prime}\right)=x+5xy^2$
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Step-by-step Solution
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- Find the derivative using the definition
- Exact Differential Equation
- Linear Differential Equation
- Separable Differential Equation
- Homogeneous Differential Equation
- Find the derivative using the product rule
- Find the derivative using the quotient rule
- Find the derivative using logarithmic differentiation
- Find the derivative
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1
Taking the derivative of arctangent
Learn how to solve implicit differentiation problems step by step online.
$\frac{1}{1+\left(4x^2y\right)^2}\frac{d}{dx}\left(4x^2y\right)=x+5xy^2$
Learn how to solve implicit differentiation problems step by step online. Find the implicit derivative d/dx(arctan(4x^2y))=x+5xy^2. Taking the derivative of arctangent. The power of a product is equal to the product of it's factors raised to the same power. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^2 and g=y.
Final answer to the problem
$4\left(\frac{1}{1+16x^{4}y^2}\right)x\left(2y+xy^{\prime}\right)=x+5xy^2$
