Find the best tutors and institutes for Class 12 Tuition
Search in
Differentiate the functions with respect to x.
Let f(x)=cos(sinx),
u(x)=sinx , v(t)=cost
Where t=u(x)=sinx
Differentiating it
Since. By chain rule,
Differentiate the functions with respect to x.
Let f(x)=sin(x2+5), u(x)=x2+5, and v(t)=sintLet f(x)=sinx2+5, ux=x2+5, and v(t)=sint
Then, (vou)=v(u(x))=v(x2+5)=tan(x2+5)=f(x)Then, vou=vux=vx2+5=tanx2+5=f(x)
Thus, f is a composite of two functions.
Alternate method
Differentiate the functions with respect to x.
Thus, f is a composite function of two functions, u and v.
Put t = u (x) = ax + b
Hence, by chain rule, we obtain
Alternate method
Differentiate the functions with respect to x.
The given function is
, where g (x) = sin (ax + b) and
h (x) = cos (cx + d)
∴ g is a composite function of two functions, u and v.
Therefore, by chain rule, we obtain
∴h is a composite function of two functions, p and q.
Put y = p (x) = cx + d
Therefore, by chain rule, we obtain
Differentiate the functions with respect to x.
Clearly, f is a composite function of two functions, u and v, such that
By using chain rule, we obtain
Alternate method
Prove that the function f given by
is notdifferentiable at x = 1
The given function is
It is known that a function f is differentiable at a point x = c in its domain if both
are finite and equal.
To check the differentiability of the given function at x = 1,
consider the left hand limit of f at x = 1
Since the left and right hand limits of f at x = 1 are not equal, f is not differentiable at x = 1
Prove that the greatest integer function defined by
is not
differentiable at x = 1 and x = 2.
The given function f is
It is known that a function f is differentiable at a point x = c in its domain if both
are finite and equal.
To check the differentiability of the given function at x = 1, consider the left hand limit of f at x = 1
Since the left and right hand limits of f at x = 1 are not equal, f is not differentiable at
x = 1
To check the differentiability of the given function at x = 2, consider the left hand limit
of f at x = 2
Since the left and right hand limits of f at x = 2 are not equal, f is not differentiable at x = 2
How helpful was it?
How can we Improve it?
Please tell us how it changed your life *
Please enter your feedback
UrbanPro.com helps you to connect with the best Class 12 Tuition in India. Post Your Requirement today and get connected.
Find best tutors for Class 12 Tuition Classes by posting a requirement.
Get started now, by booking a Free Demo Class
