When you start learning about differentiation in Year 9, there are some important rules that will help you a lot. Here’s a quick and easy summary of the most common ones:
The Power Rule: This is one of the easiest and most popular rules. If you have a function like ( f(x) = x^n ), the derivative (that’s just a fancy name for the slope or rate of change) is ( f'(x) = nx^{n-1} ). All you do is bring down the power and subtract one!
Constant Rule: If you're working with a constant (like ( f(x) = c ), where ( c ) is a number that doesn’t change), the derivative is always ( 0 ). Since constants don’t change, they have a flat slope!
Sum Rule: You can find the derivative of a sum piece by piece. If you have ( f(x) = g(x) + h(x) ), then it becomes ( f'(x) = g'(x) + h'(x) ). Nice and simple, right?
Product Rule: When you’re multiplying functions, like ( f(x) = g(x)h(x) ), the derivative is a bit more complex: ( f'(x) = g'(x)h(x) + g(x)h'(x) ).
Quotient Rule: For dividing functions, if you have ( f(x) = \frac{g(x)}{h(x)} ), the derivative looks like this: ( f'(x) = \frac{g'(x)h(x) - g(x)h'(x)}{(h(x))^2} ).
By learning and practicing these rules, you’ll build a strong base in differentiation. This will prepare you for more advanced concepts in calculus later on!
When you start learning about differentiation in Year 9, there are some important rules that will help you a lot. Here’s a quick and easy summary of the most common ones:
The Power Rule: This is one of the easiest and most popular rules. If you have a function like ( f(x) = x^n ), the derivative (that’s just a fancy name for the slope or rate of change) is ( f'(x) = nx^{n-1} ). All you do is bring down the power and subtract one!
Constant Rule: If you're working with a constant (like ( f(x) = c ), where ( c ) is a number that doesn’t change), the derivative is always ( 0 ). Since constants don’t change, they have a flat slope!
Sum Rule: You can find the derivative of a sum piece by piece. If you have ( f(x) = g(x) + h(x) ), then it becomes ( f'(x) = g'(x) + h'(x) ). Nice and simple, right?
Product Rule: When you’re multiplying functions, like ( f(x) = g(x)h(x) ), the derivative is a bit more complex: ( f'(x) = g'(x)h(x) + g(x)h'(x) ).
Quotient Rule: For dividing functions, if you have ( f(x) = \frac{g(x)}{h(x)} ), the derivative looks like this: ( f'(x) = \frac{g'(x)h(x) - g(x)h'(x)}{(h(x))^2} ).
By learning and practicing these rules, you’ll build a strong base in differentiation. This will prepare you for more advanced concepts in calculus later on!