diff --git a/docs/mhf4u7.md b/docs/mhf4u7.md index 2439c6e..0c477bd 100644 --- a/docs/mhf4u7.md +++ b/docs/mhf4u7.md @@ -440,9 +440,28 @@ results in the equation of the derivative function. Direct substitution of $h$ w The degree of a derivative is always the degree of the original function$-1$. -The power rule applies to all functions of the form $f(x)=x^n,x \in \mathbb{R}$, such that: +The **power rule** applies to all functions of the form $f(x)=x^n,x \in \mathbb{R}$, such that: $$f´(x) = nx^{n-1}$$ +??? example + $$f(x) = x^5$$ + $$f´(x) = 5x^4$$ + +The **constant multiple rule** applies to all functions of the form $f(x) = k·g(x)$, where $k$ is any real number, such that: +$$f´(x) = k·g(x)$$ + +??? example + $$f(x) = 2x^2$$ + $$f´(x) = 2·2x$$ + $$f´(x) = 4x$$ + +The **sum rule** applies to all functions of the form $f(x) = g(x) + h(x)$, where $g(x)$ and $h(x)$ are known to be differentiable, such that: +$$f´(x) = g´(x) + h´(x)$$ + +??? example + $$f(x) = 2x^2 + 3x$$ + $$f´(x) = 4x + 3$$ + ### Drawing derivative functions If the slope of a tangent is: @@ -452,7 +471,7 @@ If the slope of a tangent is: Points of inflection on the original function become maximum/minimum points on the derivative graph. -The derivative of a linear equation is always constant. +The derivative of a linear equation is always constant, and the derivative of a constant value is $0$.. ## Resources