# calc 3

Isac Portillo (lvl 3)
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$$\frac{d}{dx}[\ln u]$$

Front

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Date created

Feb 4, 2022

## Cards(18)

Unsectioned

(18 cards)

$$\frac{d}{dx}[\ln u]$$

Front

$$\frac{u'}{u}$$

Back

$$\frac{d}{dx}[\text{arccot }x]$$

Front

$$-\frac{1}{1+x^2}$$

$$x' \text{in numerator for chain rule}$$

Back

$$\frac{d}{dx}[\arctan x]$$

Front

$$\frac{1}{1+x^2}$$

$$x' \text{in numerator for chain rule}$$

Back

Chain rule short cut

Front

$$\frac{dy}{dx}n[u(x)]^{n-1}\cdot \frac{du}{dx}$$

$$\frac{dy}{dx}[u^n]=nu^{n-1}\cdot u'$$

Back

$$\frac{d}{dx}[e^u]$$

Front

$$e^u\cdot u'$$

Back

$$\frac{d}{dx}[\log_a u]$$

Front

$$\frac{1}{(\ln a)u}\cdot \frac{du}{dx}$$

Back

Trig functions chain rule

Front

$$\frac{d}{dx}[\text{trig }u]=(\text{trig }u)'\cdot u'$$

Back

$$s(t)$$

Front

Position function

Back

$$x^{-1}$$

$$f^{-1}(x)$$

Front

$$\frac{1}{x}$$

inverse of $$f(x)$$

Back

$$\frac{d}{dx}[\arcsin x]$$

Front

$$\frac{1}{\sqrt{1-x^2}}$$

$$x' \text{in numerator for chain rule}$$

Back

$$v(t)=s'(t)$$

Front

Velocity function

Back

$$\frac{d}{dx}[\arccos x]$$

Front

$$-\frac{1}{\sqrt{1-x^2}}$$

$$x' \text{in numerator for chain rule}$$

Back

$$\frac{d}{dx}[\text{arccsc }x]$$

Front

$$-\frac{1}{|x|\sqrt{x^2-1}}$$

$$x' \text{in numerator for chain rule}$$

Back

Chain rule

Front

$$\frac{d}{dx}[f(g(x))]=f'(g(x))\cdot g'(x)$$

Back

$$\frac{d}{dx}[\text{arcsec } x]$$

Front

$$\frac{1}{|x|\sqrt{x^2-1}}$$

$$x' \text{in numerator for chain rule}$$

Back

$$\frac{d}{dx}[a^u]$$

Front

$$(\ln a)a^u\cdot \frac{du}{dx}$$

Back

$$a(t)=v'(t)=s''(t)$$

Front

Acceleration function

Back

$$\frac{d}{dx}[f^{-1}(x)]$$

Front

$$\frac{1}{f'(f^{-1}(x))}$$

Back