Question

$\large\bold \red{ \frac{d}{dx} \bigg ( {5}^{4^{3 {}^{2 {}^{1} {}^{x}}}} \bigg)}$


PLEASE ANSWER MY QUESTION​

Answer 1

${ \frac{d}{dx} \bigg ( {5}^{4^{3 {}^{2 {}^{1} {}^{x}}}} \bigg)}$

$\frac{d}{dx} {5}^{{4}^{{3}^{{2}^{x}}}}$

${5}^{{4}^{{3}^{{2}^{x}}}}\ln{5}(\frac{d}{dx} {4}^{{3}^{{2}^{x}}})$

${5}^{{4}^{{3}^{{2}^{x}}}}\ln{5}\times {4}^{{3}^{{2}^{x}}}\ln{4}(\frac{d}{dx} {3}^{{2}^{x}})$

${{5}^{{4}^{{3}^{{2}^{x}}}}\ln{5}\times {4}^{{3}^{{2}^{x}}}\ln{4}\times {3}^{{2}^{x}}\ln{3}(\frac{d}{dx} {2}^{x})}$

${\ln{5}\ln{4}\ln{3}\ln{2}\times {5}^{{4}^{{3}^{{2}^{x}}}}\times {4}^{{3}^{{2}^{x}}}\times {3}^{{2}^{x}}\times {2}^{x}}$

Answer 2

Answer:

${ \frac{d}{dx} \bigg ( {5}^{4^{3 {}^{2 {}^{1} {}^{x}}}} \bigg)}$

$\frac{d}{dx} {5}^{{4}^{{3}^{{2}^{x}}}}$

${5}^{{4}^{{3}^{{2}^{x}}}}\ln{5}(\frac{d}{dx} {4}^{{3}^{{2}^{x}}})$

${5}^{{4}^{{3}^{{2}^{x}}}}\ln{5}\times {4}^{{3}^{{2}^{x}}}\ln{4}(\frac{d}{dx} {3}^{{2}^{x}})$

${{5}^{{4}^{{3}^{{2}^{x}}}}\ln{5}\times {4}^{{3}^{{2}^{x}}}\ln{4}\times {3}^{{2}^{x}}\ln{3}(\frac{d}{dx} {2}^{x})}$

${\ln{5}\ln{4}\ln{3}\ln{2}\times {5}^{{4}^{{3}^{{2}^{x}}}}\times {4}^{{3}^{{2}^{x}}}\times {3}^{{2}^{x}}\times {2}^{x}}$