Application of Differentiation – HSC Math

Posted In: Mathematics
  1. if $(x,y) is a point over line $y=f(x)$ and the slope of the line at that point $(x,y)$ is θ$, then-
    $tan\ θ=\d/\dy(y)$
    here, the tangent of the line at point $(x,y)$ creates θ° angle with $x\ axis$.
  2. If the tangent of a line is parallel to $x\ axis$ or perpendicular to $y\ axis$ then-
    $\d/\dx(y)=0$
  3. If the tangent of a line is parallel to $y-axis$ or perpendicular to $x\ axis$ then-
    $\d/\dy(x)=0$
  4. if $y=f(x)$ is a curve, then equation of the tangent on the curve at $(x_1,y_1)$ is
    $(y-y_1)=f'(x)(x-x_1)$
  5. if $y=f(x)$ is a curve, then equation of the perpendicular line on the curve at $(x_1,y_1)$ is
    $(y-y_1)=-1/{f'(x)}(x-x_1)$

Post Tags: Differentiation | HSC


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