I really need help with the following question?

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1 Answer
Feb 6, 2018

#f'(x)=4^xsec(x)(ln(4))+tan(x))#

#g'(x)=x^-4(1-3ln(x))#

Explanation:

We want to find the derivative of

#f(x)=4^xsec(x)=e^(xln(4))sec(x)#

Use the product and chain rule

#f'(x)=d/dx(e^(xln(4)))sec(x)+e^(xln(4))d/dx(sec(x))#

#=ln(4)*e^(xln(4))sec(x)+e^(xln(4))sec(x)tan(x)#

#=ln(4)*4^xsec(x)+4^xsec(x)tan(x)#

#=4^xsec(x)(ln(4))+tan(x))#

Next we want to find the derivative of

#g(x)=x^-3*ln(x)#

Use the product rule and power rule

#g'(x)=d/dx(x^-3)*ln(x)+x^-3d/dx(ln(x))#

#=-3x^-4ln(x)+x^-3*x^-1#

#=-3x^-4ln(x)+x^-4#

#=x^-4(1-3ln(x))#

Feel free to ask if anything is unclear