Derivative

Q.

$\text{If}y=2^{ax}\text{and}\frac{dy}{dx}=log256atx=1thena=$

1. 0

2. 1

3. 2

4. 3

Q.

If f(x) and g(x) have equal derivatives, then f(x) - g(x) is a ___________ function

1. Identify

2. Constant

3. Even

4. Odd

Q. lim((x+1)^4-2^4)/((2x+1)^5-3^5) x->1

Q.

If x = $e^{y+e^{y+e^{y+e^{y+...\infty }}}}$, then $\frac{dy}{dx}$ is

1. 

2. 

3. 

4. 

Q. { If }x^2-11x+30 and }x^2-9x+18 are both distinct positive }} integers, then find the integral solution of the equation }{(x^2-11x+30)^{x^2-9x+18}=(x^2-9x+18)^{x^2-11x+30

Q. If for the function $f\left(x\right)={\mathrm{kx}}^2+7x-19,f\text{'}\left(5\right)=57,$then the value of k is

Q.

If f(x) and g(x) have equal derivatives, then f(x) - g(x) is a ___________ function

1. Constant

2. Identify

3. Even

4. Odd

Q. 23, x2 +1 cos x

Q. If $2^x+2^y=2^{x+y}$ then the value of $\frac{dy}{dx}atx=y=1is$

1. \N
2. - 1
3. 1
4. 2

Q. how to solve generally integrals of form dx/((x^2+a^2)^n)

Q.

Given f(x) = g(X) . h (x) and $f^{{}^{\prime }}\left(x\right)$=$g^{{}^{\prime }}\left(x\right)$h(x) + g(x)$h^{{}^{\prime }}\left(x\right)$ find f'(x) where f(x) = x sin x.

1. sin x - x cos x

2. x sin x + cos x

3. sin x + cos x

4. sin x + x cos x

Q. What is the value of the following series ? \overset{100}{\underset{r=2}{∑(3^r(2-2r)}})/\lbrack(r+1)(r+2)\rbrack

Q.

cos a +cos (120-a)+cos (120+a)=0

Q. prove lhs equals rhs :cos theta *cos theta/2-cos 3theta*cos 9theta/2=sin 7theta/2*sin 4theta

Q. simplify:-
( root 2 - root 3i) - (- 2 - 7i)

Q.

If f(x) and g(x) have equal derivatives, then f(x) - g(x) is a ___________ function

1. Constant

2. Identify

3. Even

4. Odd

Q. Let f : [0, ∞) → R and g : R → R be defined by $f\left(x\right)=\sqrt{x}$and g(x) = x. Find f + g, f − g, fg and $\frac{f}{g}$.

Q. Prove that:
$\cos 4\theta -\cos 4\alpha =8\left(\cos \theta -\cos \alpha \right)\left(\cos \theta +\cos \alpha \right)\left(\cos \theta -\sin \alpha \right)\left(\cos \theta +\sin \alpha \right)$

Q. solve x(x-2)(x-5)/(x+3)^2(15-2x)^5<0