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Find \(\cfrac{dy}{d\mathrm x} \), when

1y = ex + 10x + xx

1 Answer

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Best answer

let y = ex + 10x + xx

⇒ y = a + b + c

where a= ex ; b = 10x ; c = x

  \(\Bigg\{\) Using chain rule, \(\cfrac{d(u +a)}{d\text x}=\cfrac{du}{d\text x}+\cfrac{da}{d\text x}\) where a and u are any variables \(\Bigg\}\)

a = ex

Taking log both the sides:

⇒ log a = log ex

⇒ log a = x log e

{log x a = a log x}

⇒ log a= x {log e =1}

Differentiating with respect to x:

Put the value of a = ex

⇒ \(\cfrac{da}{d\mathrm x} \) = a

b = 10x

Taking log both the sides:

⇒ log b= log 10x

⇒ log b= x log 10

{log xa = a log x}

Differentiating with respect to x:

  \(\Bigg\{\) Using chain rule, \(\cfrac{d(au)}{d\text x}\) = a\(\cfrac{du}{d\text x}\) where a is any constant and u is any variable \(\Bigg\}\)

Put the value of b = 10x

c = xx

Taking log both the sides:

⇒ log c= log xx

⇒ log c= x log x

{log xa = a log x}

Differentiating with respect to x:

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