MHB Find Differential Coefficient of Root 2 Sin x + 4x^5 -3/x^4

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The discussion focuses on finding the differential coefficient of the function √2 sin(x) + 4x^5 - 3/x^4. Participants clarify the expression and confirm its accuracy. There is a request for solutions, emphasizing the need for participants to share their attempts at solving the problem. Additionally, there is a suggestion to post calculus-related questions in the appropriate forum for better assistance. The conversation highlights the importance of clear communication and proper forum etiquette in academic discussions.
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1. find the differential coefficient of root 2 sin x + 4x power5 -3/x power 4

2. if y=(3x square +1)(x square + 2x) find dy/dx.
 
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rahulk said:
1. find the differential coefficient of root 2 sin x + 4x power5 -3/x power 4
Huh? Is this supposed to be [math]\sqrt{2}~sin(x) + 4 x^5 - \frac{3}{x^4}[/math]

-Dan
 
topsquark said:
Huh? Is this supposed to be [math]\sqrt{2}~sin(x) + 4 x^5 - \frac{3}{x^4}[/math]

-Dan
Yes it is true kindly slove the problem
 
rahulk said:
Yes it is true kindly slove the problem

Please show what you have tried, and please post calculus problems in our Calculus forum. :D
 

Thread 'Proving that convexity implies second order derivative being positive'

There are probably loads of proofs of this online, but I do not want to cheat. Here is my attempt: Convexity says that $$f(\lambda a + (1-\lambda)b) \leq \lambda f(a) + (1-\lambda) f(b)$$ $$f(b + \lambda(a-b)) \leq f(b) + \lambda (f(a) - f(b))$$ We know from the intermediate value theorem that there exists a ##c \in (b,a)## such that $$\frac{f(a) - f(b)}{a-b} = f'(c).$$ Hence $$f(b + \lambda(a-b)) \leq f(b) + \lambda (a - b) f'(c))$$ $$\frac{f(b + \lambda(a-b)) - f(b)}{\lambda(a-b)}...
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