Recent questions tagged differentiation

1 votes
0 answers
62
If $u=f(y-z, \: \: z-x, \: \: x-y)$, then $\frac{ \partial u}{ \partial x} + \frac{ \partial u}{ \partial y} + \frac{ \partial u}{ \partial z} $ is equal to:$x+y+z$$1+x+...
2 votes
2 answers
66
Let $g: \mathbb{R} \rightarrow \mathbb{R}$ be differentiable with $g'(x^2)=x^3$ for all $x>0$ and $g(1) =1$. Then $g(4)$ equals$64/5$$32/5$$37/5$$67/5$
1 votes
0 answers
68
Let $x$ and $y$ be real numbers satisfying $9x^2+16y^2=1$. Then $(x+y)$ is maximum when$y=9x/16$$y=-9x/16$$y=4x/3$$y=-4x/3$
0 votes
0 answers
70
Why is a function not differentiable at x=k when f'(x) limits to infinity? Limit can be infinite too?
3 votes
1 answer
74
Which of the following is the derivative of $f(x)=x^{x}$ when $x>0$ ?$x^{x}$$x^{x} \ln \;x$$x^{x}+x^{x}\ln\;x$$(x^{x}) (x^{x}\ln\;x)$$\text{None of the above; function is...
0 votes
1 answer
80
5 votes
1 answer
81
$n$-th derivative of $x^n$ is$nx^{n-1}$$n^n.n!$$nx^n!$$n!$
36 votes
5 answers
82
Let $f(x)$ be a polynomial and $g(x)=f'(x)$ be its derivative. If the degree of $(f(x)+f(-x))$ is $10$, then the degree of $(g(x) - g(-x))$ is __________.
2 votes
1 answer
85
Let $f: \mathbb{R} \to \mathbb{R}$ be a differentiable function such that $\displaystyle \lim_{x \to +\infty} f'(x)=1$, then$f$ is bounded $f$ is increasing $f$ is unboun...
1 votes
1 answer
86
The derivative of the function$\int_{0}^{\sqrt{x}} e^{-t^{2}}dt$at $x = 1$ is $e^{-1}$ .
2 votes
1 answer
88
The differential equation$\frac{dy}{dx}= y^{1/3}, y(0)=0$ hasA unique solutionNo nontrivial solution Finite number of solutionsInfinite number of solutions
4 votes
4 answers
89