Question

Find dy/dx if y=10^x^x + 10^x^10 + 10^10^x

Answer 1

ANSWER:

$2x { \big({10}^{x} \big) }^{x} + {10}^{x + 1} { \big({10}^{x} \big) }^{10} + log( {10}^{10} ) { \big({10}^{10} \big) }^{x}$

GIVEN:

$y = { \big({10}^{x} \big) }^{x} + { \big({10}^{x} \big) }^{10} + { \big({10}^{10} \big) }^{x}$

TO FIND:

dy / dx

FORMULAE:

log (xⁿ) = n log(x)

d/dx [log(x)] = 1/x

$\frac{d}{dx} \big( {a}^{x} \big) = {a}^{x} log(a)$

d/dx(uv) = uv' + vu'

d/dx(constant) = 0

log 10 = 1

NOTE: CALCULATION IS IN ATTACHMENT.