What is the d/(dθ)(ln({x}(θ))(-θ-2)) ?

The d/(dθ)(ln({x}(θ))(-θ-2)) is (d/(dθ)({x}(θ))(-θ-2))/({x)(θ)}-ln({x}(θ))

What is the first d/(dθ)(ln({x}(θ))(-θ-2)) ?

The first d/(dθ)(ln({x}(θ))(-θ-2)) is (d/(dθ)({x}(θ))(-θ-2))/({x)(θ)}-ln({x}(θ))

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\frac{d}{d θ} (ln (x (θ)) (- θ - 2))

\frac{\frac{d}{d θ} ( x ( θ ) ) ( - θ - 2 )}{x ( θ )} - ln (x (θ))

Solution steps

\frac{d}{d θ} (ln (x (θ)) (- θ - 2))

Apply the Product Rule:

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

f = ln (x (θ)), g = - θ - 2

= \frac{d}{d θ} (ln (x (θ))) (- θ - 2) + \frac{d}{d θ} (- θ - 2) ln (x (θ))

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

\frac{d}{d θ} (- θ - 2) = - 1

= \frac{\frac{d}{d θ} ( x ( θ ) )}{x ( θ )} (- θ - 2) + (- 1) ln (x (θ))

Simplify

\frac{\frac{d}{d θ} ( x ( θ ) )}{x ( θ )} (- θ - 2) + (- 1) ln (x (θ)) : \frac{\frac{d}{d θ} ( x ( θ ) ) ( - θ - 2 )}{x ( θ )} - ln (x (θ))

= \frac{\frac{d}{d θ} ( x ( θ ) ) ( - θ - 2 )}{x ( θ )} - ln (x (θ))

\int - csc^{2} (\frac{9 x}{8}) d x

\int e^{u} d u

9 \cdot x^{2} \cdot y^{^{'}} = y^{^{'}} + 7 \cdot x \cdot e^{- y}

f (x) = 6 x^{\frac{4}{3}} - \frac{2}{3} x^{\frac{3}{2}} + x^{2} - 7 x + 1

\frac{d}{d x} (cos^{2} (\frac{x}{2}))

What is the d/(dθ)(ln({x}(θ))(-θ-2)) ?
The d/(dθ)(ln({x}(θ))(-θ-2)) is (d/(dθ)({x}(θ))(-θ-2))/({x)(θ)}-ln({x}(θ))
What is the first d/(dθ)(ln({x}(θ))(-θ-2)) ?
The first d/(dθ)(ln({x}(θ))(-θ-2)) is (d/(dθ)({x}(θ))(-θ-2))/({x)(θ)}-ln({x}(θ))