# Calculus Part 2

posted by .

y = tan(sqrtx)
Find dy/dx.
So I found it and I got the answer as sec^2(sqrtx) but the answer is (sec^2(sqrtx))/2(sqrtx)...why?
----------------------------------

2) Find the line which passes through the point (0, 1/4) and is tangent to the curve y=x^3 at some point.
So I found the derivative which is 3x^2.
Let (a, a3) be the point of tangency.

3x^2 = (a3 - 1/4)/(a-0)
I'm not sure how to solve for a.

Can someone please help me out with these? I have an exam tomorrow evening and these questions are a lost cause.

• Calculus Part 2 -

y = tan u
dy/dx = sec^2 u du/ dx
here u = x^(1/2)
du/dx = sec^2 (x^.5) .5 x^-.5
=(1/2) (1/sqrt x) sec^2(sqrt x)
I agree with the authorities.

• Calculus Part 2 -

2) Find the line which passes through the point (0, 1/4) and is tangent to the curve y=x^3 at some point.
So I found the derivative which is 3x^2.
Let (a, a3) be the point of tangency.

3x^2 = (a3 - 1/4)/(a-0)
I'm not sure how to solve for a.
--------------------------------
sketching that I see no such line. Are you sure it is not through (1/4 , 0)

## Similar Questions

1. ### Integration

Intergrate ¡ì sec^3(x) dx could anybody please check this answer. are the steps correct?

Suppose a publishing company has found that the marginal cost at a level of production of x thoudsand books is given by: C'(x)=50/sqrroot(x) and the fixed cost is \$25,000. Find the cost function C(x). C= INT C'= INT 50/sqrtx= 100 sqrtx …
3. ### math

Please help me simplify: 4sqrtx^12/24sqrtx^2 *Is this correct: 2sqrt4/12x The answer you get depends upon where you put the parentheses, and you don't show any. I don't see any way of coming up with your answer. 4 (sqrtx)^12/ 24 (sqrtx)^2 …
4. ### Calculus

lim(x->infinity) sqrtx sin(1/sqrtx) Someone please start me off. I don't know how to find the limits of trigonometric functions.
5. ### calculus

tangent line and normal line of y=(sqrtx)/(x+1) when p=(4,2/5)
6. ### Calculus

I don't know how to do the integral of e^(lnx^2)dx and the integral of (sin sqrtx)/(sqrtx) dx
7. ### Calc

Find the equation of the tangent line to f(x)=sqrtx^2+6x at x=2, give your answer in slope-intercept form
8. ### Algebra

1. Solve log(4/x) (x^2 - 6) = 2. (note: the (4/x) is underscored) 2. Show that loga [(x + {sqrtx^2-5}) / 5] = -loga (x - (sqrtx^2-5))
9. ### Applied Calc

Find the indefinite integral of (1-sqrtx)/(1+sqrtx)dx I just worked completely through this problem using substitution (u=1+sqrtx) and came to the answer 3+4sqrtx+x+C. This is incorrect. Not sure where I messed up.
10. ### Calculus Math

Find the height of y=((sqrtx)(3-x))/3 for 0<=x<=3 Use the arc length formula and note that 1/4x+1/2+x/4=(1/(2sqrtx) + sqrtx/x)^2 is a perfect suare.

More Similar Questions