Finding more derivatives

[Joyci116]

Homework Statement

a.) f(x)=tan²(x)

b.) cos³(x²)

c.) (2x-1)/(5x+2)

d.) (sqrt(x²-2x))(secx)

e.) f(x)=((2x+3)/(x+7))^3/2

f.) [sin(x)cos(x)]²

Homework Equations

chain rule
Product rule
Quotient rule
Power rule

The Attempt at a Solution

a.) would you do the power rule for this? 2tanx
b.) this is a combination of the chain rule and the power rule?
-3sinx²*2x
c.) use the quotient rule
((5x+2)(2)-(2x-1)(5))/(5x+2)²

((10x+2)-(10x-5))/(5x+2)²

7/(5x+2)²

d.) use the chain rule and the product rule?
Use the chain rule for the first pararenthasis. And then use the product rule?
f.) used the chain rule
2sinxcosx*(-cosxsinx)

 

[PShooter1337]

a) this is actually both chain and product rule. tan$^{2}$x is the same as (tanx)$^{2}$.
So now you use power rule on the entire function, multiplied by the derivative of the function, i.e. 2tanxsec$^{2}$x

b) Again, chain rule and power rule. cos$^{3}$(x$^{2}$) can be rewritten as (cos(x$^{2}$))$^{3}$, which, when differentiated, becomes
3(cos(x$^{2}$))$^{2}$(-sin(x$^{2}$))(2x)

c) Looks right

d) yes

e) Combination quotient rule / power rule / chain rule. first differentiate as if it were a single variable, then differentiate what's inside using quotient rule.

f) the first part looks right, 2sinxcosx, but the 2nd part doesn't. The 2nd part should basically be (d/dx)(sinxcosx) which is product rule, i.e. cos$^{2}$x - sin$^{2}$x

 

[Joyci116]

thank you.

 

[berkeman]

a) this is actually both chain and product rule. tan$^{2}$x is the same as (tanx)$^{2}$.
So now you use power rule on the entire function, multiplied by the derivative of the function, i.e. 2tanxsec$^{2}$x

b) Again, chain rule and power rule. cos$^{3}$(x$^{2}$) can be rewritten as (cos(x$^{2}$))$^{3}$, which, when differentiated, becomes
3(cos(x$^{2}$))$^{2}$(-sin(x$^{2}$))(2x)

c) Looks right

d) yes

e) Combination quotient rule / power rule / chain rule. first differentiate as if it were a single variable, then differentiate what's inside using quotient rule.

f) the first part looks right, 2sinxcosx, but the 2nd part doesn't. The 2nd part should basically be (d/dx)(sinxcosx) which is product rule, i.e. cos$^{2}$x - sin$^{2}$x

Don't provide solutions here in the future. It violates the PF rules that you agreed to when you joined here.