What is the derivative of ln(y+y^2+cos(x)) ?

The derivative of ln(y+y^2+cos(x)) is ((dy)/(dx))/y+2y(dy)/(dx)-sin(x)

What is the first derivative of ln(y+y^2+cos(x)) ?

The first derivative of ln(y+y^2+cos(x)) is ((dy)/(dx))/y+2y(dy)/(dx)-sin(x)

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

\frac{\frac{d y}{d x}}{y} + 2 y \frac{d y}{d x} - sin (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (ln (y)) = \frac{\frac{d y}{d x}}{y}

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

\frac{d}{d x} (cos (x)) = - sin (x)

= \frac{\frac{d y}{d x}}{y} + 2 y \frac{d y}{d x} - sin (x)

y^{^{''}} + 2 y^{^{'}} + y = sin (2 t)

\int_{- \infty}^{6} x e^{\frac{x}{2}} d x

y^{^{'}} = \frac{1}{1 + y}

x^{2} (1 - 3 x)

x \to 1 lim (- (3))

What is the derivative of ln(y+y^2+cos(x)) ?
The derivative of ln(y+y^2+cos(x)) is ((dy)/(dx))/y+2y(dy)/(dx)-sin(x)
What is the first derivative of ln(y+y^2+cos(x)) ?
The first derivative of ln(y+y^2+cos(x)) is ((dy)/(dx))/y+2y(dy)/(dx)-sin(x)