Question

Y=x3*√2/(1+x) ребята помогите найти производную сложной функции.

Answer 1

X^3*sqrt(2/1+x)
F'(x)=3x^2sqrt(2/1+x)-x^3*1/2*sqrt(x+1)/sqrt(2)*2*1/(x+1)^2=

=x^2*sqrt(2/1+x)(3-x/2*(x+1))=((5x+6)*x^2/(x+1))*sqrt(1/2(1+x))

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Answer 2

I can help you with finding the derivative of a complex function. Here is the solution:

To find the derivative of $$Y=x^3\sqrt{2/(1+x)}$$, we can use the product rule and the chain rule. The product rule states that if $$f(x)$$ and $$g(x)$$ are two functions, then $$f'(x)g(x)+f(x)g'(x)$$ is the derivative of their product. The chain rule states that if $$h(x)$$ is a function of another function $$u(x)$$, then $$h'(x)=h'(u(x))u'(x)$$ is the derivative of the composite function.

Let $$f(x)=x^3$$ and $$g(x)=\sqrt{2/(1+x)}$$. Then $$f'(x)=3x^2$$ and $$g'(x)=-\frac{1}{\sqrt{2(1+x)^3}}$$ by applying the chain rule to $$g(x)$$. Therefore, the derivative of $$Y$$ is:

$$Y'=(x^3)(-\frac{1}{\sqrt{2(1+x)^3}})+(3x^2)(\sqrt{2/(1+x)})$$

We can simplify this expression by multiplying both terms by $$\sqrt{2(1+x)^3}$$ and getting a common denominator:

$$Y'=\frac{-2x^3+6x^5+6x^2}{\sqrt{2(1+x)^3}}$$

This is the final answer. I hope this helps you understand how to find the derivative of a complex function.Y=x3*√2/(1+x)+ребята+помогите+найти+производную+сложной+функции.+