What is the d/(dθ)(({r}(θ))(1+sec(θ))sin(θ)) ?

The d/(dθ)(({r}(θ))(1+sec(θ))sin(θ)) is d/(dθ)({r}(θ))(1+sec(θ))sin(θ)+(cos(θ)+sec^2(θ)){r}(θ)

What is the first d/(dθ)(({r}(θ))(1+sec(θ))sin(θ)) ?

The first d/(dθ)(({r}(θ))(1+sec(θ))sin(θ)) is d/(dθ)({r}(θ))(1+sec(θ))sin(θ)+(cos(θ)+sec^2(θ)){r}(θ)

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\frac{d}{d θ} ((r (θ)) (1 + sec (θ)) sin (θ))

\frac{d}{d θ} (r (θ)) (1 + sec (θ)) sin (θ) + (cos (θ) + sec^{2} (θ)) r (θ)

Solution steps

\frac{d}{d θ} ((r (θ)) (1 + sec (θ)) sin (θ))

Apply the Product Rule:

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

f = r (θ), g = (1 + sec (θ)) sin (θ)

= \frac{d}{d θ} (r (θ)) (1 + sec (θ)) sin (θ) + \frac{d}{d θ} ((1 + sec (θ)) sin (θ)) r (θ)

\frac{d}{d θ} ((1 + sec (θ)) sin (θ)) = cos (θ) + sec^{2} (θ)

= \frac{d}{d θ} (r (θ)) (1 + sec (θ)) sin (θ) + (cos (θ) + sec^{2} (θ)) r (θ)

\frac{( 3 x ^{2} + 10 y ^{4} ) ^{2}}{16}

(sin (2 θ) + 2 sin (θ)) (1 - cos (θ))

x (x - 10 x)

\frac{( sin ( x ) e ^{x} ) - ( e ^{x} \cdot cos ( x ) )}{( sin ( x ) ) ^{2}}

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What is the d/(dθ)(({r}(θ))(1+sec(θ))sin(θ)) ?
The d/(dθ)(({r}(θ))(1+sec(θ))sin(θ)) is d/(dθ)({r}(θ))(1+sec(θ))sin(θ)+(cos(θ)+sec^2(θ)){r}(θ)
What is the first d/(dθ)(({r}(θ))(1+sec(θ))sin(θ)) ?
The first d/(dθ)(({r}(θ))(1+sec(θ))sin(θ)) is d/(dθ)({r}(θ))(1+sec(θ))sin(θ)+(cos(θ)+sec^2(θ)){r}(θ)