What is the d/(dθ)((t)(cot(θ)y(t,θ))) ?

The d/(dθ)((t)(cot(θ)y(t,θ))) is t((-csc^2(θ)){y}(t,θ)+d/(dθ)({y}(t,θ))cot(θ))

What is the first d/(dθ)((t)(cot(θ)y(t,θ))) ?

The first d/(dθ)((t)(cot(θ)y(t,θ))) is t((-csc^2(θ)){y}(t,θ)+d/(dθ)({y}(t,θ))cot(θ))

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\frac{d}{d θ} ((t) (cot (θ) y (t, θ)))

t ((- csc^{2} (θ)) y (t, θ) + \frac{d}{d θ} (y (t, θ)) cot (θ))

Solution steps

\frac{d}{d θ} ((t) (cot (θ) y (t, θ)))

Treat

t

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= t \frac{d}{d θ} (cot (θ) y (t, θ))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cot (θ), g = y (t, θ)

= t (\frac{d}{d θ} (cot (θ)) y (t, θ) + \frac{d}{d θ} (y (t, θ)) cot (θ))

\frac{d}{d θ} (cot (θ)) = - csc^{2} (θ)

= t ((- csc^{2} (θ)) y (t, θ) + \frac{d}{d θ} (y (t, θ)) cot (θ))

- \frac{1}{5} x^{2} + 2 x - 4

(- 12 n) + (- 21)

\frac{- 12}{7}

x y^{'} (x) + (ln (x)) y

What is the d/(dθ)((t)(cot(θ)y(t,θ))) ?
The d/(dθ)((t)(cot(θ)y(t,θ))) is t((-csc^2(θ)){y}(t,θ)+d/(dθ)({y}(t,θ))cot(θ))
What is the first d/(dθ)((t)(cot(θ)y(t,θ))) ?
The first d/(dθ)((t)(cot(θ)y(t,θ))) is t((-csc^2(θ)){y}(t,θ)+d/(dθ)({y}(t,θ))cot(θ))