Differenciation Multiple choice questions

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Differenciation Multiple choice questions consist of 50+ Multiple Choice Questions. Prepare these mcqs for Fsc, ECAT and other examinations. These mcqs are very helpful for preparing NTS and PPSC exams. The mcqs were uploaded on daily basis so keep visiting this website. ONCE the material is completely uploaded then Explanation of each mcqs and videos will be provided very soon.
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Q.1    \lim_{\delta x \rightarrow 0} \frac{f(a+\delta x)-f(a)}{\delta x} =

(a)     f ‘ (x)

(b)     f ‘ (a)

(c)     f ‘ (2)

(d)     f ‘ ( 0)

Check Answer
b

Q.2  \lim_{\delta x \rightarrow 0} \frac{f(x+\delta x)-f(x)}{\delta x} =

(a)     0

(b)     f ‘ (x)

(c)     f ‘ (2)

(d)     Not defined

Check Answer
b

Q.3 \lim_{\delta x \rightarrow 0} \frac{f(0+\delta x)-f(0)}{\delta x} =

(a)     f ‘ (x)

(b)     f ‘ (a)

(c)     f ‘ (2)

(d)     f ‘ ( 0)

Check Answer
d

Q.4  \lim_{\delta x \rightarrow 0} \frac{f(2+\delta x)-f(2)}{\delta x} =

(a)     f ‘ (x)

(b)     f ‘ (a)

(c)     f ‘ (2)

(d)     f ‘ ( 0)

Check Answer
c

Q.5  \lim_{ x \rightarrow a} \frac{f(x)-f(0)}{x-a} =

(a)     f ‘ (x)

(b)     f ‘ (a)

(c)     f ‘ (2)

(d)     f ‘ ( 0)

Check Answer
a

Q.6 If  f(x)  =x^{\frac{2}{3}}  ,  then f'(8)=

(a)      1/2

(b)     2/3

(c)     1/3

(d)     3

(Gujranwala board, 2005)

Check Answer
c

Q.7 \frac{d}{dx}(x^n) =

(a)  nx^{n-1}

(b)  -nx^{n-1}

(c)    (n-1)x^{n-1}

(d)     \frac{x^{n-1}}{n+1}

Check Answer
a

Q.8    \frac{d}{dx}(x^n - 2) =

(a)  n(x^{n-1}-2)

(b)  (n-2)x^{n-1}

(c)  (n-1)x^{n-1}

(d)  nx^{n-1}

Check Answer
d

Q.9    \frac{d}{dx}(x^2)=

(a)     x²

(b)   x³

(c)    2x

(d)    x

Check Answer
c

Q.10  \frac{d}{dx}(ax+b)^n =

(a)    n(ax^{n-1}+b)

(b)    n(ax^{n-1}+b)^{n-1}

(c)    nax^{n-1}

(d)    na(ax+b)^{n-1}

Check Answer
d

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