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Question
Differentiate the following w.r.t.x :
y = `7^x + x^7 - 2/3 xsqrt(x) - logx + 7^7`
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Solution
y = `7^x + x^7 - 2/3 xsqrt(x) - logx + 7^7`
Differentiating w.r.t. x, we get
`("d"y)/("d"x) = "d"/("d"x) (7^x + x^7 - 2/3 xsqrt(x) - log x + 7^7)`
∴ `("d"y)/("d"x) = "d"/("d"x) (7^x) + "d"/("d"x) (x^7) - 2/3 "d"/("d"x) (x^(3/2)) - "d"/("d"x) (logx) + "d"/("d"x) 7^7`
= `7^x log 7 + 7x^6 - 2/3 xx 3/2 x^(3/2 - 1) - 1/x + 0`
= `7^x log 7 + 7x^6 - x^(1/2) - 1/x`
= `7^x log 7 + 7x^6 - sqrt(x) - 1/x`
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