d/dx((2^xcotx)/sqrt2) = (2^x (cotx(ln2)-csc^2x))/sqrt2 Let's use the product rule: d/dx(ab) = b(da)/dx + a(db)/dx ...

Explanation: From the given equation #f (x)=csc x- sin x# We determine #f'' (x)#, the second derivative of #f (x)#

Q&A and Videos that make learning easy. Math, History, Chemistry, Algebra, Calculus, Biology and more.

The first half is quite easy, just bring the 4 to the front and change the power to 3. # (dy)/ (dx)=4 (csc (6sqrt (x)))^3*f' (x)# The derivative of #csc (g (x))=-g' (x)csc (g (x))cot (g (x))# Here, #g (x)=6sqrt (x) …

However, we cannot differentiate a non implicit function of #y# wrt #x#. But if we apply the chain rule we can differentiate a function of #y# wrt #y# but we must also multiply the result by #dy/dx#.

Questions and Videos on Differentiating Inverse Trigonometric Functions, within Calculus

Questions and Videos on Notation for the Second Derivative, within Calculus

Q&A and Videos that make learning easy. Math, History, Chemistry, Algebra, Calculus, Biology and more.

How do you integrate ∫ 1 √3x − 12√x + 53 using trigonometric substitution?

Q&A and Videos that make learning easy. Math, History, Chemistry, Algebra, Calculus, Biology and more.