Download App

Derivatives — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsDerivatives5 Marks
Question
Differentiate the following function with respect to x:$\log_{\text{x}^2}\text{x}$
✓

Answer

$\log_{\text{x}^2}\text{x}=\frac{\log\text{x}}{\log\text{x}^2}$ (By change of base property)$=\frac{\log\text{x}}{2\log\text{x}}[\log\text{x}^2=2\log\text{x}]$
$=\frac{1}{2}$
Now $\frac{\text{d}}{\text{dx}}(\log_{\text{x}^2}\text{x})=\frac{\text{d}}{\text{dx}}\Big(\frac{1}{2}\Big)$
$=0(\because\frac{1}{2}$ is a constant)

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Derivatives→Derivatives — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{1-\cos4\text{x}}{\text{x}^2}$
→
Prove that the family of lines represented by $\text{x}(1+\lambda)=\text{y}(2-\lambda)+5=0,$ $\lambda$ being arbitrary, pass through a fixed point. Also, find that point.
→
Prove that:
$\frac{\sin\text{A}+\sin\text3{A}}{\cos\text{A}-\cos3\text{A}}=\cot\text{A}$
→
Rewrite the following statement with “if$-$then” in five different ways conveying the same meaning.
If a natural number is odd, then its square is also odd.
→
Sketch the graphs of the following functions:
$\text{f(x)}=\text{cosec}^2\text{x}$
→
If a, b, c are in A.P. b, c, d are in G.P. and $\frac{1}{\text{c}},\frac{1}{\text{d}},\frac{1}{\text{e}}$ are in A.P., prove that a, c, e are in G.P.
→
Find the complex number satisfying the equation $\text{z}+\sqrt{2}|(\text{z}+1)|+\text{i}=0$
→
If |z + 1| = z + 2(1 + i), then find z.
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{x}^2+1-\cos\text{x}}{\text{x}\sin\text{x}}$
→
In the following match each item given under the $\text{column}\  C_1$ to its correct answer given under the $\text{column}\  C_2$:
  $\text{column}\  C_1$   $\text{column}\  C_2$
$(a)$ $\sin(\text{x + y})\sin\text{x}-\text{y}$ $(i)$ $\cos^2\text{x}-\sin^2\text{y}$
$(b)$ $\cos(\text{x + y})\cos(\text{x}-\text{y})$ $(ii)$ $\frac{1-\tan\theta}{1+\tan\theta}$
$(c)$ $\cot\Big(\frac{\pi}{4}+\theta\Big)$ $(iii)$ $\frac{1+\tan\theta}{1-\tan\theta}$
$(d)$ $\tan\Big(\frac{\pi}{4}+\theta\Big)$ $(iv)$ $\sin^2\text{x}-\sin^2\text{y}$
→