Fundamentals of Differentiation

$\csc^2(x)$

$\sec^2(x)$

$\cos^2(x)$

$\tan(x)$

$\frac{dy}{d\theta}=\tan(x)\csc(x)$

$\frac{dy}{d\theta}=\sin(\theta)\csc(\theta)$

$\frac{dy}{dx}=-\csc(\theta)\cot(\theta)$

$\frac{dy}{d\theta}=\csc(\theta)\cot(\theta)$

1+\sqrt{2}

-\sqrt{2}-1

1-\sqrt{2}

\sqrt{2}-1

INCORRECT 3. $-\csc^2(x)\cot(x)$

CORRECT. $2\sec^2(x)\tan(x)$

INCORRECT 1. $\sec^2(x) + 2\tan^2(x)$

INCORRECT 2. $\sec^4(x)$

$\frac{df}{d\theta} = -2\cot(\theta)\csc^2(\theta)$

$\frac{df}{d\theta} = 2\tan(\theta)\sin^2(\theta)$

$\frac{df}{d\theta} = -\cot(\theta)^{-1}\csc^3(\theta)$

$\frac{df}{d\theta} = -2\csc(\theta)\cot^2(\theta)$

$g'(t) = -(1 + 2t)\csc^2(t^2 + t + 1)$

$g'(t) = -(1+ t)^{-2}$

$g'(t) = -\sin(t^2+t+1)/\cos^3(t^2+t+1)$

$g'(t) = (1 + 2t)\csc^2(t^2 + t + 1)$

$\cos^2(x)$

$-\sec^2(x)$

$\sec^2(x)$

$\sin^2(x)$

$h''(x)=15 x^{3}\tan(9 x^{8})$

$h''(x)=60x^{3}\sec^{2}(3 x^{4})(12 x^{3})$

$h''(x)=20 x^{3}\sin(9 x^8)$

$h''(x)-60x ^ {3 }\sec ^ {2 }(\sin (x))$

$y' = \frac{1}{\cos^2(x)}$

$y' = -\sec(x)\tan(x)$

$y' = \sec(x)\tan(x)$

$y' = \csc(x)\cot(x)$

$-\csc^2\left(\frac{\pi}{4}\right)$

$\sin\left(\frac{\pi}{4}\right) \cos\left(\frac{\pi}{4}\right)$

$\tan\left(\frac{\pi}{4}\right)$

$\sec^2\left(\frac{\pi}{4}\right)$