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Question
Differentiate the following w.r.t.x :
y = `3 cotx - 5"e"^x + 3logx - 4/(x^(3/4))`
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Solution
Let y = `3 cotx - 5"e"^x + 3logx - 4/(x^(3/4))`
∴ `("d"y)/("d"x) = "d"/("d"x) [3 cot x - 5"e"^x + 3 log x - 4x^(-3/4)]`
= `"d"/("d"x) (3 cot x) - "d"/("d"x) (5"e"^x) + "d"/("d"x) (3 log x) - "d"/("d"x) (4x^(-3/4))`
= `3 "d"/("d"x) (cot x) - 5 "d"/("d"x) ("e"^x) + 3"d"/("d"x) (log x) - 4 "d"/("d"x) (x^(-3/4))`
= `3 xx (- "cosec"^2x) - 5"e"^x + 3 xx 1/x - 4 xx (-3/4)x^(-7/4)`
= `- 3 "cosec"^2x - 5"e"^x + 3/x + 3/(x^(7/4)`
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