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Question
Differentiate the following w.r.t.x. :
y = `x^2sqrt(x) + x^4logx`
Sum
Solution
y = `x^2sqrt(x) + x^4logx`
Differentiating w.r.t. x, we get
`("d"y)/("d"x) = "d"/("d"x) (x^2 sqrt(x) + x^4 log x)`
`("d"y)/("d"x) = "d"/("d"x) (x^(5/2)) + "d"/("d"x) (x^4 log * x)`
= `5/2x^(5/2 - 1) + [x^4 "d"/("d"x) log x + log x("d"/("d"x) x^4)]`
= `5/2x^(3/2) + [x^4 (1/x) + log x(4x^3)]`
= `5/2x^(3/2) + x^3 (1 + 4logx)`
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Derivative of Logarithmic Functions
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Chapter 9: Differentiation - Exercise 9.2 [Page 192]
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