What is the derivative of 2x+2yy^'(x) ?

The derivative of 2x+2yy^'(x) is 2+2(y^{1+'}+(1+')x(dy)/(dx)y^')

What is the first derivative of 2x+2yy^'(x) ?

The first derivative of 2x+2yy^'(x) is 2+2(y^{1+'}+(1+')x(dy)/(dx)y^')

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

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

Solution steps

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

Simplify

2 x + 2 y y^{^{'}} (x) : 2 x + 2 x y^{1 +^{'}}

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (2 x) = 2

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

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

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5 - (3 (cos (x)))

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y - 3 (2)^{x} - 2

What is the derivative of 2x+2yy^'(x) ?
The derivative of 2x+2yy^'(x) is 2+2(y^{1+'}+(1+')x(dy)/(dx)y^')
What is the first derivative of 2x+2yy^'(x) ?
The first derivative of 2x+2yy^'(x) is 2+2(y^{1+'}+(1+')x(dy)/(dx)y^')