Question
Download Solution PDFयदि f(x) = ecos x है, तो f(x) का अवकलज क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
अवकलज नियम:
माना कि y = ef(x) है, तो
\(\rm \dfrac {dy}{dx} = e^{f(x)} \dfrac {d}{dx} f(x)\)
गणना:
दिया गया है, f(x) = ecos x
दोनों पक्ष पर x के संबंध में अवकलज लेने पर, हमें निम्न प्राप्त होता है
⇒ f'(x) = \(\rm \dfrac {d}{dx}\)(ecos x)
⇒ f'(x) = ecos x \(\rm \dfrac {d}{dx} (\cos x)\)
⇒ f'(x) = ecos x (- sin x)
⇒ f'(x) = (- sin x)ecos x
अतः यदि f(x) = ecos x है, तो f(x) का अवकलज (- sin x)ecos x है।
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