Differentiate the following w-r-t- x- -x - 3-

The correct option is B 12(x+3)^ 1/2 d dx ( √( x+3 ) #160; ) = d dx ( x+3 ) #160; ^ 1/2 = 1 2 ( x+3 ) #160; ^ 1/2 1 ( d dx ( x+3 ...

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Standard XII

Mathematics

Special Integrals - 2

Differentiate...

Question

Differentiate the following w.r.t. $x$ .
$\sqrt{x + 3}$ .

\frac{1}{3} (x + 3)^{- 1 / 2}

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\frac{1}{2} (x + 3)^{- 1 / 2}

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\frac{1}{2} (x + 3)^{- 3 / 2}

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\frac{3}{2} (x + 3)^{- 1 / 2}

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Solution

The correct option is B $\frac{1}{2} (x + 3)^{- 1 / 2}$
$\frac{d}{d x} (\sqrt{x + 3})$
$= \frac{d}{d x} {(x + 3)}^{1 / 2}$
$= \frac{1}{2} {(x + 3)}^{1 / 2 - 1} (\frac{d}{d x} (x + 3))$
$= \frac{1}{2} {(x + 3)}^{- 1 / 2} . (1 + 0)$
$= \frac{1}{2} {(x + 3)}^{- 1 / 2}$

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Similar questions

3 [\frac{3 x - 1}{2 x + 3}] - 2 [\frac{2 x + 3}{3 x - 1}] = 5; x \neq \frac{1}{3}, - \frac{3}{2}

Q. Prove the following :

∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} x^{3} & {3 x}^{2} & 3 x & 1 x^{2} & x^{2} + 2 x & 2 x + 1 & 1 x & 2 x + 1 & x + 2 & 1 1 & 3 & 3 & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ = {(x - 1)}^{6} .

Q. If

∣ ∣ ∣ ∣ ∣ \begin{matrix} x^{2} + x & x + 1 & x - 2 2 x^{2} + 3 x - 1 & 3 x & 3 x - 3 x^{2} + 2 x + 3 & 2 x - 1 & 2 x - 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

= Ax+B then

Solve :

$(i) \frac{1}{3} x - 6 = \frac{5}{2} (i i) \frac{2 x}{3} - \frac{3 x}{8} = \frac{7}{12} (i i i) (x + 2) (x + 3) + (x - 3) (x - 2) - 2 x (x + 1) = 0 (i v) \frac{1}{10} - \frac{7}{x} = 35 (v) 13 (x - 4) - 3 (x - 9) - 4 (x + 4) = 0 (v i) x + 7 - \frac{8 x}{3} = \frac{17 x}{6} - \frac{5 x}{8} (v i i) \frac{3 x - 2}{4} - \frac{2 x + 3}{3} = \frac{2}{3} - x (v i i i) \frac{x + 2}{6} - (\frac{11 - x}{3} - \frac{1}{4}) = \frac{3 x - 4}{12} (i x) \frac{2}{5 x} - \frac{5}{3 x} = \frac{1}{15} (x) \frac{x + 2}{3} - \frac{x + 1}{5} = \frac{x - 3}{4} - 1 (x i) \frac{3 x - 2}{3} + \frac{2 x + 3}{2} = x + \frac{7}{6} (x i i) x - \frac{x - 1}{2} = 1 - \frac{x - 2}{3} (x i i i) \frac{9 x + 7}{2} - (x - \frac{x - 2}{7}) = 36 (x i v) \frac{6 x + 1}{2} + 1 = \frac{7 x - 3}{3}$

Q. Solve the equations:

\frac{2 x^{3} - 3 x^{2} + x + 1}{2 x^{3} - 3 x^{2} - x - 1} = \frac{3 x^{3} - x^{2} + 5 x - 13}{3 x^{3} - x^{2} - 5 x + 13}

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Differentiate the following w.r.t. x.√x+3.

The correct option is B 12(x+3)−1/2ddx(√x+3)=ddx(x+3)1/2=12(x+3)1/2−1(ddx(x+3))=12(x+3)−1/2.(1+0)=12(x+3)−1/2

Differentiate the following w.r.t. $x$ .
$\sqrt{x + 3}$ .

The correct option is B $\frac{1}{2} (x + 3)^{- 1 / 2}$
$\frac{d}{d x} (\sqrt{x + 3})$
$= \frac{d}{d x} {(x + 3)}^{1 / 2}$
$= \frac{1}{2} {(x + 3)}^{1 / 2 - 1} (\frac{d}{d x} (x + 3))$
$= \frac{1}{2} {(x + 3)}^{- 1 / 2} . (1 + 0)$
$= \frac{1}{2} {(x + 3)}^{- 1 / 2}$