What is differentiation and what does it actually mean?
Differentiation is the process of finding the rate of change of a function with respect to its independent variable. In simpler terms, by differentiating, you can find the gradient of a curve. If its a straight line, then the the gradient of the the graph, as you go along the x-axis, doesn't change meaning that by differentiating the equation of the line, we get a constant value!Keeping this in mind, differentiation must be something we can do to an equation to get its gradient, and it is. To differentiate we multiply by the power currently applied to X and then reduce the power applied to X by one.
Example: Differentiate the following, with respect to x.y=x3+c
well, the first part is easy, we follow the rule:
dy/dx =2x1 + 0
so how come its '+0' ? Well c is a constant and all constants differentiate to zero because you can re-write c as;c = cx0and when we differentiate this we end up with0cx-1And we all know that 0 multiplied by anything is 0.
Related Maths GCSE answers
All answers ▸The perimeter of an isosceles triangle is 16cm. One of the sides equals to x+3, while the unequal one equals to x+4. Calculate the area of this triangle.
There are n sweets in a bag. 6 of them are orange, the rest are yellow. Hannah takes a random sweet, she eats the sweet and repeats again. The probability that hannah eats two orange sweets is 1/3. Show that n2 - n - 90 = 0.
Solve the simultaneous equations 5x+y=21 and x-2y=9
S is a geometric sequence. a) Given that (√x - 1), 1, and (√x + 1) are the first three terms of S, find the value of x. b) Show that the 5th term of S is 7 + 5√2