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: