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m_a_m_a [10]
2 years ago
8

Find the derivative of the function. y = sin−1(6x + 1)

Mathematics
1 answer:
liraira [26]2 years ago
7 0

If you don't know the derivative of the inverse of sine, you can use implicit differentiation. Apply sine to both sides:

y=\sin^{-1}(6x+1)\implies\sin y=6x+1

(true for <em>y</em> between -π/2 and π/2)

Now take the derivative of both sides and solve for it:

\cos y\dfrac{\mathrm dy}{\mathrm dx}=6

\dfrac{\mathrm dy}{\mathrm dx}=6\sec y

\dfrac{\mathrm dy}{\mathrm dx}=\dfrac6{\cos\left(\sin^{-1}(6x+1)\right)}

\dfrac{\mathrm dy}{\mathrm dx}=\dfrac6{\sqrt{1-(6x+1)^2}}

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