y' (x) = color (blue) (-csc (5x)csc^2x - 5cotxcot (5x)csc (5x) We're asked to find the derivative (dy)/ (dx) [y = (cotx)/ (sin (5x))] We can first use the quotient ...

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

While the cosecant has a tabled, standard derivative we can work with the sine too, if you don't remember / don't have a standard derivative table handy.

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Questions and Videos on Differentiating Inverse Trigonometric Functions, within Calculus

How are sin (x), tan (x), and x related graphically? How can I find the derivative of #y=c^x# using first principles, where c is an integer? What is the derivative of #log_e (x)#? What are the …

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#.

The third one is dy/dx = (2x)/(3y^2) and the value is 1/3 So from y^3 - x^2 = 4 We take the derivative as normal d/dx(y^3) - d/dx(x^2) = d/dx(4) d/dx(y^3) - 2x = 0 d/dx(y^3) = 2x Using the …

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

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