Differentiating is the act of finding the derivative of a function, thus allowing you to find out how the function changes as its input changes, such as finding the rate of change of the gradient of the function, and when differentiating with respect to time can allow you to give equations explaining the motion of various objects, depending on how you differentiate the functions. There are two main types of differentiation, ordinary differentiation and partial differentiation, the rules outlined below are for ordinary differentiation. While the rules for partial differentiation are not that dissimilar, they do not need to be known outside of university level mathematics and physics.
(using f' and g' to denote the derivative of the functions f and g of x respectively, x is a variable, o indicates a composite function, all other letters are constants, rules in bold are important)
Elementary rulesf = xn, f' = nx(n-1) elementary power rule
f = a, f' = 0 constant rule
f = ax, f' = a derivative of a linear function is a constant
(af +bg)' = af'+bg' linearity of differentiation, leading to the 3 following,
(af)' = af' constant multiple rule
(f+g)' = f'+g' sum rule
(f-g)' = f'-g' subtraction rule,
(fg)' = f'g + fg' product rule
(fog)' = (f(g))' = (f'(g))g' = (f'og)g' chain rule
f = 1/g, f' = -g'/g2 reciprocal rule
(f/g)' = (f'g-fg')/g2 quotient rule
f=sin(x), f'=cos(x)
f=cos(x), f'=-sin(x)
f=tan(x), f'=sec2(x)
f=sec(x), f'=sec(x)tan(x)
f=cosec(x) f'=-cosec(x)cot(x)
f=cot(x), f'=-cosec2(x)
f=exp(ax), f'=a*exp(ax)
f=exp(axn), f'=anx(n-1)*exp(axn)
f=ax, f'=(log(a))*ax
f=log(x), f'=1/x
f=log(xn), f'=nx(n-1)/xn
f=xx, f'=xx(1+log(x))
these are just the simple rules of differentiation for various functions, there are a LOT more, but they are generally only of use at university levels.
Subjective part of science
a process in which a number, quantity, expression, etc., is altered or manipulated according to formal rules, such as those of addition, multiplication, and differentiation.
a process in which a number, quantity, expression, etc., is altered or manipulated according to formal rules, such as those of addition, multiplication, and differentiation.
See related link below for a good explanation
Differentiation of funtion is rate of chnage of that funtion.
cell differentiation
There is no such thing as cheating within the rules. If you cheat that is pure cheating and there is no explanation . If you are true to someone then you are true to them.
You learn the rules for differentiating polynomials, products, quotients, etc. Then you learn the chain rule and a couple of other rules and you're good to go for the basics. You can check your results by learning to use wolframalpha.com.
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Implicit differentiation is a special case of the well-known rules of derivatives. Using implicit differentiation would be beneficial in math equations.
Subjective part of science
See link for explanation and examples.
scientific explanation is....... wait why am i answering this... i dont know is the answer...
no
differentiation.
a process in which a number, quantity, expression, etc., is altered or manipulated according to formal rules, such as those of addition, multiplication, and differentiation.
a process in which a number, quantity, expression, etc., is altered or manipulated according to formal rules, such as those of addition, multiplication, and differentiation.