The differentiation of the function f(x) = sin⁻¹(3x⁵) is [tex]15x^4/\sqrt{1-9x^{10}}[/tex].
What is function?
Function is a combination of different types of variable and constants.
A function is denoted by f(x).
The given function is,
f(x) = sin⁻¹(3x⁵)
Differentiate the given function with respect to x
f'(x) = d/dx(sin⁻¹(3x⁵))
The differentiation of sin⁻¹x is [tex]1/\sqrt{1-x^2}[/tex],
f'(x) =[tex]1/\sqrt{1-(3x^5)^2}\cdot d/dx(3x^5)[/tex]
= [tex]1/\sqrt{1-9x^{10}}\cdot 15x^4[/tex]
= [tex]15x^4/\sqrt{1-9x^{10}}[/tex]
The differentiation of f(x) = sin⁻¹(3x⁵) is [tex]15x^4/\sqrt{1-9x^{10}}[/tex].
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