Calculus Flashcards
What is a derivative
Derivative of a function = dy/dx = slope at a point
It gives us the instantaneous rate of change of a function.
Eg. If derivative of a function = 5x, then the instantaneous rate of change of that function when x=3, would be 15.
Why is the derivative of a constant value 0
For a constant function, say c, The value of y remains same as long as x stays constant say “c”
Which means f’(c) = 0
Derivative of a constant is always
0 ,because in the graph: when we check the slope at any point is 0.
In a graph in which y=x³ the slope at any point in the graph (derivative) :
3x³⁻¹ = 3x²
This rule is called the power rule.
When you take f(x) = C (a constant) the slope of it is
So it means that whatever value you give for x , the value of the y (fx) coordinate always has the same value 7. As there is no change in the y coordinate , the slope is 0.
The shape of the graph when y = f(x) = x²
Parabola
To find the indefinite integral of a f(x) means
Finding the anti derivative of f(x)
That would be another function.
Reverse power rule
∫x³ dx = (x ³⁺¹)/3+1 + C
An angle in xy plane, is said to be in its standard form, when
The vertex is at the origin and the initial ray lies also get the positive x axis.
Sin of 37
3/5
Sin of 53
4/5
Cos of 37
4/5
Tangent
Straight line touching a curve at a particular point.
If c is a constant d/dx of c =
0
Derivative of x³ is
3x³⁻¹ = 3x²
This rule is called the power rule.
d/dx (Cx) =
C d/dx (x)
This rule is called constant multiple rule
The derivative of the negative of a differentiable function is the negative of the function’s derivative
d/dx (-u) = -1 d/dx(u)
Derivative of the sum of 2 differentiable functions is the sum of their derivatives.
This rule is called
The sum rule:
d/dx(u-v) = d/dx(u) - d/dx(v)
In prime notation :
‘ (derivative)
″ (double derivative)
‴ (third derivative)
⁗ (fourth derivative)
