CBSE BoardEnglish MediumSTD 11 ScienceMathsDerivatives3 Marks
Question
Differentiate the following functions with respect to x:$\frac{10^\text{x}}{\sin\text{x}}$
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Answer
We have,$\frac{\text{d}}{\text{dx}}\Big(\frac{10^\text{x}}{\sin\text{x}}\Big)$
Using quotient rule, we get
$\frac{(\sin\text{x})\frac{\text{d}}{\text{dx}}(10^\text{x})-(10^\text{x})\frac{\text{d}}{\text{dx}}(\sin\text{x})}{(\sin\text{x})^2}$
$=\frac{\sin\text{x}\times10^\text{x}\log10-10^\text{x}\cos\text{x}}{(\sin\text{x})^2}$
$=10^\text{x}\text{cosecx}\log10-10^\text{x}\text{cosecx}\cot\text{x}$
$=10^\text{x}\text{cosecx}(\log10-\cot\text{x})$
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