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Derive the function arcsin((x^0.5+3)/(sin(x^2))) with respect to x

\frac{d}{dx}\left(arcsin\left(\frac{\sqrt{x}+3}{\sin\left(x^2\right)}\right)\right)

Step by step solution

Problem

$\frac{d}{dx}\left(arcsin\left(\frac{\sqrt{x}+3}{\sin\left(x^2\right)}\right)\right)$

Show full step-by-step solution

Answer

$\frac{\frac{1}{2}x^{-\frac{1}{2}}\sin\left(x^2\right)-2x\left(3+\sqrt{x}\right)\cos\left(x^2\right)}{\sin\left(x^2\right)^2\sqrt{1-\frac{\left(3+\sqrt{x}\right)^2}{\sin\left(x^2\right)^2}}}$

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$\frac{d}{dx}\left(arcsin\left(\frac{\sqrt{x}+3}{\sin\left(x^2\right)}\right)\right)$

Main topic:

Differential calculus

Used formulas:

4. See formulas

Time to solve it:

0.44 seconds