# calculus

posted by .

differentiate f(x)=Tan^3(e^2x +1)

• calculus -

Let v(x) = e^2x + 1
dv/dx= 2 e^2x
Let u(v) = tan^3 v

f(x) = u[(v(x)]
df/dx = du/dv * dv/dx

For du/dv, let f(g) = g^3 and
g(v) = tan v

u = f{g(v)}
du/dv = df/dg * dg/dv = 3 g^2 * sec^2(v)
= 3 tan^2v*sec^2(v)

df/dx= 2e^(2x)*3tan^2v*sec^2(v)

Substitute e^2x +1 for v for the derivative imn terms of x.

## Similar Questions

1. ### calculus

can anyone tell me if tan-1x= 1 over tan x?
2. ### calculus

Differentiate e^(2x^3+x) X tan(x^2) tan e^x / ln(x^6/2-3x+3e) cos(tan(e^4x^2))
3. ### trigo help!

1. differentiate cos(3/x) 2. differentiate sin(4/x) 3. differentiate 3/{sin(3x+pi)} 4. differentiate pxsin(q/x)where p and q are constants. 5. differentiate xsin(a/x) where a is constant 6. differentiate sec^3(3x^2+1)
4. ### calculus

Differentiate the following function. f (x) = 6 x 2 sin(x)tan(x) Where do I begin?
5. ### Calculus

I think I have the correct answers for the following problems. For anyone who has the time I would appreciate it if you could tell me if I am correct/incorrect. Thank you. 1). Differentiate ã(x)sin x = (2xcosx+sinx)/2ã(x) 2). …
6. ### calculus

a billboard 20ft tall is located on top of a building with its lower edge 60 ft above the level of a viewers eye. how far from a point directly below the sign should a viewer stand to maximize the angle (theta) between the lines of …
7. ### Calculus

I'm having problems with this one. Can't get the right answer. Differentiate the following using the chain rule. f(x) = squareroot(x^2+1)/(3x+1) I know that I can take the whole thing and put it to the (1/2) and differentiate that …
8. ### calculus

If limit as delta x approaches 0 of tan(0+Δx)-tan(0)/Δx =1 which of the following is false: d/dx [tanx]=1 the slope of y = tan(x) at x = 0 is 1 y = tan(x) is continuous at x = 0 y = tan(x) is differentiable at x = 0
9. ### calculus

5. Find the equation of the tangent line to the graph of f(a) = -sec(a) at the point (0, -1) 6. Differentiate y = sin(x)tan(x). 7. Find f '(x) for f(x) = sin(x)cot(x). 8. Find the derivative of the function f(x) = cos^2(x) + tan^2(x) …
10. ### Calculus

differentiate tan-1(2x/1-x^2)

More Similar Questions