Question

differentiate 10^x¹⁰​

Answer 1

Answer:

100x^9.............

Answer 2

Differentiation of a function of the form f(x) = a^x is given by a^x.ln(a)

Let f(x) = 10^x^10

Let x^10 = u

Differentiate u = x^10 with respect to x,

u' = 10x^9 .......................................(i)

Now, the function is f(u) = 10^u

Differentiate with respect to u,

f'(u) = a^u.ln(u)

f'(u) = a^(x^10).ln(x^10) .....................(ii)

Multiply (i) and (ii),

f'(u).u' = [10x^9][a^(x^10).ln(x^10)]

f'(x) = 10a^(x^10).ln(x^10).x^9

Thus, the answer is: 10a^(x^10).ln(x^10).x^9