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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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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\ln\left(x\right)$ and $g=\cos\left(xy\right)$
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$\frac{d}{dx}\left(\ln\left(x\right)\right)\cos\left(xy\right)+\ln\left(x\right)\frac{d}{dx}\left(\cos\left(xy\right)\right)=1$
Learn how to solve problems step by step online. Find the implicit derivative d/dx(ln(x)cos(xy))=1. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\ln\left(x\right) and g=\cos\left(xy\right). The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=y. Simplify the product -(\frac{d}{dx}\left(x\right)y+x\frac{d}{dx}\left(y\right)).
