Quotient Rule of Differentiation

Q. $\int \frac{3\cos x+2}{\sin x+2\cos x+3}dx$

Q.

Divide $60a^{2}by12a^2$.

Q.

Differentiate $x^{2}tanx.$

Q. Suppose $f$ and $g$ are differentiable functions on $(0,\infty )$ such that $f\text{'}\left(x\right)=-\frac{g\left(x\right)}{x}$ and $g\text{'}\left(x\right)=-\frac{f\left(x\right)}{x}$, for all $x>0$. Further, $f\left(1\right)=3$ and $g\left(1\right)=-1$.

If $f\left(x\right)-g\left(x\right)=B{x}^m,$ for all $x>0$ and some constant $B$, then the value of $m$ equals

1. $1$
2. $2$
3. $1$
4. $-2$

Q. ax+b8.

Q.

Express the algebraic expression $\frac{16{\mathrm{x}}^2{\mathrm{y}}^2}{24{\mathrm{xy}}^3}$in its lowest form.

Q. If $y=(1+x)(1+x^2)(1+x^4)\cdots (1+x^{2^n})$ then $\frac{dy}{dx}$ at x = 0 is

1. \N
2. -1
3. 1
4. None of these

Q. 7ax2 +bx+c