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BRAD5IN
Answered

1. What does it mean when we say "the derivative measures the slope of
the tangent lines"?
2. How are derivatives related to the slope of the tangent line?
3. Give at least three scenarios in a real-life situation where the
derivative of functions is applicable?​

Sagot :

BISAYAROSEMARIEDUMALIN

Answer:

The Derivative tells us the slope of a function at any point.

slope examples y=3, slope=0; y=2x, slope=2

There are rules we can follow to find many derivatives.

For example:

The slope of a constant value (like 3) is always 0

The slope of a line like 2x is 2, or 3x is 3 etc

and so on.

Here are useful rules to help you work out the derivatives of many functions (with examples below). Note: the little mark ’ means derivative of, and f and g are functions.

Common Functions Function

Derivative

Constant c 0

Line x 1

ax a

Square x2 2x

Square Root √x (½)x-½

Exponential ex ex

ax ln(a) ax

Logarithms ln(x) 1/x

loga(x) 1 / (x ln(a))

Trigonometry (x is in radians) sin(x) cos(x)

cos(x) −sin(x)

tan(x) sec2(x)

Inverse Trigonometry sin-1(x) 1/√(1−x2)

cos-1(x) −1/√(1−x2)

tan-1(x) 1/(1+x2)

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