What is the derivative of sin^2((x^2+1/x)) ?

The derivative of sin^2((x^2+1/x)) is (sin((2(1+x^2))/x)(-1+x^2))/(x^2)

What is the first derivative of sin^2((x^2+1/x)) ?

The first derivative of sin^2((x^2+1/x)) is (sin((2(1+x^2))/x)(-1+x^2))/(x^2)

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\frac{d}{d x} (sin^{2} (\frac{x ^{2} + 1}{x}))

\frac{sin ( \frac{2 ( 1 + x ^{2} )}{x} ) ( - 1 + x ^{2} )}{x ^{2}}

Solution steps

\frac{d}{d x} (sin^{2} (\frac{x ^{2} + 1}{x}))

Apply the chain rule:

2 sin (\frac{x ^{2} + 1}{x}) \frac{d}{d x} (sin (\frac{x ^{2} + 1}{x}))

= 2 sin (\frac{x ^{2} + 1}{x}) \frac{d}{d x} (sin (\frac{x ^{2} + 1}{x}))

\frac{d}{d x} (sin (\frac{x ^{2} + 1}{x})) = \frac{cos ( \frac{x ^{2} + 1}{x} ) ( x ^{2} - 1 )}{x ^{2}}

= 2 sin (\frac{x ^{2} + 1}{x}) \frac{cos ( \frac{x ^{2} + 1}{x} ) ( x ^{2} - 1 )}{x ^{2}}

Simplify

2 sin (\frac{x ^{2} + 1}{x}) \frac{cos ( \frac{x ^{2} + 1}{x} ) ( x ^{2} - 1 )}{x ^{2}} : \frac{sin ( \frac{2 ( 1 + x ^{2} )}{x} ) ( - 1 + x ^{2} )}{x ^{2}}

= \frac{sin ( \frac{2 ( 1 + x ^{2} )}{x} ) ( - 1 + x ^{2} )}{x ^{2}}

x \to 4 - lim (\frac{1}{4 - x})

\frac{11}{( 2 x ^{3} - 5 ) ^{4}}

\int \frac{x ^{5} + 2}{x ^{2} - 1} d x

\frac{d}{d x} (sin (x) \cdot cos (x))

y^{^{''}} + 9 y = 2 cos (3 x), y (0) = 1, y^{^{'}} (0) = 0

What is the derivative of sin^2((x^2+1/x)) ?
The derivative of sin^2((x^2+1/x)) is (sin((2(1+x^2))/x)(-1+x^2))/(x^2)
What is the first derivative of sin^2((x^2+1/x)) ?
The first derivative of sin^2((x^2+1/x)) is (sin((2(1+x^2))/x)(-1+x^2))/(x^2)