What is the d/(dθ)(({r}(θ))(e^{3θ})) ?

The d/(dθ)(({r}(θ))(e^{3θ})) is d/(dθ)({r}(θ))e^{3θ}+e^{3θ}*3{r}(θ)

What is the first d/(dθ)(({r}(θ))(e^{3θ})) ?

The first d/(dθ)(({r}(θ))(e^{3θ})) is d/(dθ)({r}(θ))e^{3θ}+e^{3θ}*3{r}(θ)

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\frac{d}{d θ} ((r (θ)) (e^{3 θ}))

\frac{d}{d θ} (r (θ)) e^{3 θ} + e^{3 θ} \cdot 3 r (θ)

Solution steps

\frac{d}{d θ} ((r (θ)) (e^{3 θ}))

Apply the Product Rule:

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

f = r (θ), g = e^{3 θ}

= \frac{d}{d θ} (r (θ)) e^{3 θ} + \frac{d}{d θ} (e^{3 θ}) r (θ)

\frac{d}{d θ} (e^{3 θ}) = e^{3 θ} \cdot 3

= \frac{d}{d θ} (r (θ)) e^{3 θ} + e^{3 θ} \cdot 3 r (θ)

x^{7} - x^{7}

4 (h + 5)^{2} + 20 (h + 5) + 25

- x^{16} z^{16} + y^{16}

8 x - 8 y + a x - a y

\frac{3 ( 73 )}{2}

What is the d/(dθ)(({r}(θ))(e^{3θ})) ?
The d/(dθ)(({r}(θ))(e^{3θ})) is d/(dθ)({r}(θ))e^{3θ}+e^{3θ}*3{r}(θ)
What is the first d/(dθ)(({r}(θ))(e^{3θ})) ?
The first d/(dθ)(({r}(θ))(e^{3θ})) is d/(dθ)({r}(θ))e^{3θ}+e^{3θ}*3{r}(θ)