Question

y=x^3.5^x find dy/dx

Answer 1

y= x³.5^x

we know,
when, y = f(x).g(x) then,
dy/dx = g(x)df(x)/dx + f(x).dg(x)/dx

also we know,
when y = a^x where a is constant then,
dy/dx = a^x.lna

solution:-

y = x³.5^x
dy/dx =5^x.d(x³)/dx + x³.d(5^x)/dx
= 5^x.3x² + x³.5^x.ln5
= x²(3.5^x + x.ln5.5^x)

Answer 2

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