What is the derivative of θtan(θ) ?

The derivative of θtan(θ) is tan(θ)+θsec^2(θ)

What is the first derivative of θtan(θ) ?

The first derivative of θtan(θ) is tan(θ)+θsec^2(θ)

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derivative of

θ tan (θ)

tan (θ) + θ sec^{2} (θ)

Solution steps

\frac{d}{d θ} (θ tan (θ))

Apply the Product Rule:

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

f = θ, g = tan (θ)

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

\frac{d}{d θ} (θ) = 1

\frac{d}{d θ} (tan (θ)) = sec^{2} (θ)

= 1 \cdot tan (θ) + sec^{2} (θ) θ

Simplify

= tan (θ) + θ sec^{2} (θ)

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\int \frac{4 x - 3}{11 + 10 x - x ^{2}} d x

What is the derivative of θtan(θ) ?
The derivative of θtan(θ) is tan(θ)+θsec^2(θ)
What is the first derivative of θtan(θ) ?
The first derivative of θtan(θ) is tan(θ)+θsec^2(θ)