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Using the Quotient rule, Find dy/dx given that y = sec(x)

d[sec(x)]/dx -->d[1/cos(x)] -->( [d[1].cos(x) - d[cos(x)].1] ) / [cos(x)]^2 -->[0.cos(x) - -sin(x).1]/ [cos(x)]^2 -->sin(x)/[cos(x)]^2 -->tan(x)sec(x) <-- Final Answer
RK
Answered by Rakib K. • Maths tutor
4676 Views

Find the integral of y= e^3x / 1+e^x using calculus.

First, you use the substitution u=1+e x which implies that du=e x dx. Then, you factorise e 3x = e 2x e x and replace e x dx with du. Then by rearranging, e 2x = (u-1) 2 , so you are now ready to substitute ...
AI
Answered by Aliki I. • Maths tutor
19676 Views

Find the integral of y=6/(e^x+2) using calculus.

First, use the substitution u=e^x (which implies dx=du/u) to make the integral ∫6/(u*(u+2)))du. Next seperate the fraction using partial fractions and expand to form 3∫1/u du - 3∫1/(u+2) du. Next integrate t...
JP
Answered by Jonathan P. • Maths tutor
5524 Views

How do I integrate ln(x)?

This is a very cunning application of the integration by parts rule. Although it might look at first like integration by parts doesn't apply here since there is only the one factor, there is actually a hidde...
SP
Answered by Seb P. • Maths tutor
4025 Views

∫6e^(2x+1) dx, find integral

6 ∫ e^(2x+1) dx 6 ∫ (1/2)(e^(2x+1))3e^(2x+1) + c
DY
Answered by Dila Y. • Maths tutor
9832 Views