U3 formulas

What is the derivative of inverse sine (arcsin)?

1/√(1-x^2)

What is the derivative of inverse cosine (arccos)?

-1/√(1-x^2)

What is the derivative of inverse tangent (arctan)?

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

What is the derivative of inverse cosecant (arccsc)?

$$-1/x√x^2-1$$

What is the derivative of inverse secant (arcsec)?

$$\frac{1}{x\text{√}(x^2-1)}$$

What is the derivative of inverse cotangent (arccot)?

-1/1+x²

How do you calculate the derivative of an inverse function?

1/f’(f^-1(x))

How do you calculate the derivative of an inverse function g(x)?

1/f’(g(x))

What is the logarithmic identity for the product of two variables?

$$\text{log}_b(u \times v) = \text{log}_b(u) + \text{log}_b(v)$$

What is the logarithmic identity for the quotient of two variables?

$$\text{log}_b\bigg(\frac{u}{v}\bigg) = \text{log}_b(u) - \text{log}_b(v)$$

What is the logarithmic identity for an exponent?

$$\text{log}_b(x^k) = k \times \text{log}_b(x)$$

What is the derivative of the natural logarithm ln(x)?

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

What is the derivative of the logarithm of base b, log_b(x)?

$$\frac{1}{x\text{ln}(b)}$$

What is the derivative of a raised to the power of 4?

a^4lna

What is the derivative of a raised to the power of g(x)?

a^g(x)lna

What does the Mean Value Theorem state?

$$f'(c) = \frac{f(b)-f(a)}{b-a}$$

What is the linear approximation L(x) around a point a?

$$L(x) = f(a) + f'(a)(x-a)$$

What is ln(e^x)?

$$x$$

What is e raised to the power of ln(x)?

$$x$$

What is the value of ln(e)?

$$1$$

What is the value of ln(1)?

$$0$$