What is the d/(dθ)(θsin(θ)) ?

The d/(dθ)(θsin(θ)) is sin(θ)+θcos(θ)

What is the first d/(dθ)(θsin(θ)) ?

The first d/(dθ)(θsin(θ)) is sin(θ)+θcos(θ)

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\frac{d}{d θ} (θ sin (θ))

sin (θ) + θ cos (θ)

Solution steps

\frac{d}{d θ} (θ sin (θ))

Apply the Product Rule:

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

f = θ, g = sin (θ)

= \frac{d}{d θ} (θ) sin (θ) + \frac{d}{d θ} (sin (θ)) θ

\frac{d}{d θ} (θ) = 1

\frac{d}{d θ} (sin (θ)) = cos (θ)

= 1 \cdot sin (θ) + cos (θ) θ

Simplify

= sin (θ) + θ cos (θ)

x^{2} + 3 x - 2

\frac{d ^{3}}{d x ^{3}} (arctan (x))

- 0.1 x^{2} - x + 40

\int 7 x e^{(3 x - 1)} d x

n = 1 \sum \infty \frac{n !}{10 8 ^{n}}