Question

a) find the derivative of x^{cos}^{(x^2)} using
any method.

b) find the derivative of f(x) = sqrt(3-x) using only the definition.

Answer #1

use
the definition of derivative to find the derivative of
f(x)= 2*sqrt(x-7)
show work please.

Using the definition of the derivative, find f'(x). let f(x) =
x^2/x+1

Let f(x)=3x2+10x+3.
a) Find the derivative of f(x) using the definition of the
derivative.
b) Find the equation of the tangent line at point x=−1

Find the derivative using the definition:
A) f(x) = 1 if x is less than or equal to 1
and x^2 if x > 1
B) f(x)= x+2/x-3

Please Find: f(x)=x2+2
1) The derivative of f(x) using the limit definition:
2) The instantaneous rate of change at x=3:
3) The equation of the tangent line at x=3:
Please write out all the steps clearly.

Find the derivative of the function using the definition of
derivative.
g(x) =
sqrt 9 −
x
g' (x) =
State the domain of the function. (using interval notation.)
State the domain of its derivative. (using interval notation.)

use the definition of the derivative to find
f′(3) if f(x) = x^2 - 2x

Consider f(x) = x2 – 8x. Find its derivative using
the limit definition of the derivative. Simplify all
steps.
a. Find f(x + h).
____________
b. Find f(x + h) – f(x).
____________
c. Find [f(x + h) – f(x)] ÷ h.
____________
d. Find lim (hà0) [f(x + h) – f(x)] ÷ h.
____________
e. Find an equation of the line tangent to
the graph of y = x2 – 8x where x = -3. Present your
answer...

Find the root of f(x) = exp(x)sin(x) - xcos(x) by the
Newton’s method
starting with an initial value of xo = 1.0.
Solve by using Newton’method until satisfying the tolerance
limits of the followings;
i. tolerance = 0.01
ii. tolerance = 0.001
iii. tolerance= 0.0001
Comment on the results!

Show that the derivative of f(x) = 6+4x^2 is f' (x)=8x by using
the definition of the derivative as the limit of a difference
quotient.

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