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Question
Differentiate the following w.r.t.x :
y = `log x - "cosec" x + 5^x - 3/(x^(3/2))`
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Solution
y = `log x - "cosec" x + 5^x - 3/(x^(3/2))`
Differentiating w.r.t. x, we get
`("d"y)/("d"x) = "d"/("d"x)(log x - "cosec" x + 5^x - 3/(x^(3/2)))`
∴ `("d"y)/("d"x) = "d"/("d"x)(logx) - "d"/("d"x) ("cosec" x) + "d"/("d"x)(5^x) - 3"d"/("d"x)(x^(-3/2))`
= `1/x - (- "cosec" x cot x) + 5^x log 5 - 3(-3/2 x^((-3)/2 - 1))`
= `1/x - (- "cosec" x cot x) + 5^x log 5 - 3(-3/2 x^((-5)/2))`
= `1/x + "cosec" x cot x + 5^x log 5 + 9/(2x^(5/2))`
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