I asked as this did not seem the right chain rule use. If i understood the problem correctly.youngstudent16 said:Derivative of the outside multiplied by the derivative of the inside
(f*g)'=(f'*g)+(g'*f)
Where f=f(x)
g=(x+g(x))
I'm getting 40 but not sure if I attempted this correctly
This has been written wrong .youngstudent16 said:So f'(x)(x+g(x))[(1+g'(x))(f(x)]
2(0+1)(1+3)(5)=40
Ahhhh. Much better.Qwertywerty said:This has been written wrong .
d( f(x+g(x)) )/dx = f'(x+g(x))*(1+g'(x)) .
Qwertywerty said:This has been written wrong .
d( f(x+g(x)) )/dx = f'(x+g(x))*(1+g'(x)) .
Well you don't know anything about the function f, but solving for x=0 does just mean f'(0+g(0)).youngstudent16 said:f'(x+g(x))
How do I solve this with the given information? Would it just be the derivative f a constant which makes the whole thing 0?
I don't follow you .youngstudent16 said:Would it just be the derivative f a constant which makes the whole thing 0?
I would plug in the value for x and g(0) getting derivative of 1 which is 0. Making the final answer 0.Qwertywerty said:I don't follow you .
but f'(1) is not zero by the conditions above.youngstudent16 said:I would plug in the value for x and g(0) getting derivative of 1 which is 0. Making the final answer 0.
I think that's right I really confused myself on the chain rule
You don't find derivative by putting the value before differentiating .youngstudent16 said:I would plug in the value for x and g(0) getting derivative of 1 which is 0. Making the final answer 0
Lok said:but f'(1) is not zero by the conditions above.
My suggestion to you is that you revise differentiation once again .youngstudent16 said:oh wow that x=1 did come in handy I got it finally 12 was correct
thanks for the patience really helped with the my confusion
The chain rule is a formula used to find the derivative of a composite function. It is important because many functions in mathematics and science are composed of multiple functions, and the chain rule allows us to find the rate of change of these composite functions.
To apply the chain rule, you must first identify the inner and outer functions of the composite function. Then, you take the derivative of the outer function and multiply it by the derivative of the inner function, treating the inner function as a variable.
For example, if we have the function f(x) = (x^2 + 1)^3, we can rewrite it as f(x) = g(h(x)) where g(x) = x^3 and h(x) = x^2 + 1. To find the derivative of f(x), we would use the chain rule: f'(x) = g'(h(x)) * h'(x) = 3(x^2 + 1)^2 * 2x = 6x(x^2 + 1)^2.
Yes, there are some special cases where the chain rule may need to be modified. For example, if the outer function is a logarithmic or exponential function, we must use the chain rule with the natural logarithm or exponential function respectively.
The chain rule has many real-world applications, such as in physics and engineering. For example, in physics, the chain rule can be used to find the velocity of an object with changing acceleration, or the rate of change of a temperature with respect to time in thermodynamics. It is also used in economics and finance to find the marginal cost and marginal revenue of a business.