Evaluate and simplify z ′ z^{\prime} given t = sin ⁡ ( t + z ) t = \sin(t + z) .

z ′ = sec ⁡ ( t + z ) − 1 z^{\prime}=\sec\left(t+z\right)-1

z ′ = cos ⁡ ( t + z ) − 1 z^{\prime}=\cos\left(t+z\right)-1

z ′ = sec ⁡ ( t + z ) + 1 z^{\prime}=\sec\left(t+z\right)+1

z ′ = cos ⁡ ( t + z ) + 1 z^{\prime}=\cos\left(t+z\right)+1

Implicit Differentiation

5. Applications of Derivatives / Implicit Differentiation / Problem 4

Problem 4

Evaluate and simplify $z^{'}$ given $t = \sin (t + z)$ .

$z^{'} = \cos (t + z) - 1$

$z^{'} = \sec (t + z) + 1$

$z^{'} = \sec (t + z) - 1$

$z^{'} = \cos (t + z) + 1$