Let F(x) = ƒ(x) g(x) h(x) for all real x, where ƒ(x), g(x) and h(x) are differentiable

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Let ƒ(x) be a real differentiable function such that ƒ(0) = 1 and ƒ(x + y) = ƒ(x)ƒ'(y) + ƒ'(x) ƒ(y)

Let 𝒇(𝒙)=𝒙|𝒙|;𝒙∈𝐑. Discuss its differentiability at 𝒙=𝟎.

Let \( f, g:[0,1] \rightarrow R \) are differentiable functions wit...

A Proof that Differentiable Functions are Continuous

Let f:R-R, g:R-R and h:R-R be differentiable functions such f(x)=x^3+3x+2, g(f(x))=x & h(g(g(x)))=x

Given a differentiable function `f(x)` defined for all real `x`, and is such that `f(x+h)-f(x)

Let \( f, g:[0,1] \rightarrow R \) are differentiable functions wit...

If both `f(x) & g(x)` are differentiable functions at `x=x_0`then the function defiend as `h...