What is the derivative of sin(t/(sqrt(t+9))) ?

The derivative of sin(t/(sqrt(t+9))) is (cos(t/(sqrt(t+9)))(t+18))/(2(t+9)sqrt(t+9))

What is the first derivative of sin(t/(sqrt(t+9))) ?

The first derivative of sin(t/(sqrt(t+9))) is (cos(t/(sqrt(t+9)))(t+18))/(2(t+9)sqrt(t+9))

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derivative of

sin (\frac{t}{t + 9})

\frac{cos ( \frac{t}{t + 9} ) ( t + 18 )}{2 ( t + 9 ) t + 9}

Solution steps

\frac{d}{d t} (sin (\frac{t}{t + 9}))

Apply the chain rule:

cos (\frac{t}{t + 9}) \frac{d}{d t} (\frac{t}{t + 9})

= cos (\frac{t}{t + 9}) \frac{d}{d t} (\frac{t}{t + 9})

\frac{d}{d t} (\frac{t}{t + 9}) = \frac{t + 18}{2 ( t + 9 ) t + 9}

= cos (\frac{t}{t + 9}) \frac{t + 18}{2 ( t + 9 ) t + 9}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{cos ( \frac{t}{t + 9} ) ( t + 18 )}{2 ( t + 9 ) t + 9}

\int \frac{2 x + 1}{3 x ^{2} - 27} d x

\int \frac{1}{e ^{- x} + 1} d x

\int \frac{1}{2 + 7 y ^{2}} d y

e^{- 2 t}

\frac{d}{d x} (\frac{5}{x + 4})

What is the derivative of sin(t/(sqrt(t+9))) ?
The derivative of sin(t/(sqrt(t+9))) is (cos(t/(sqrt(t+9)))(t+18))/(2(t+9)sqrt(t+9))
What is the first derivative of sin(t/(sqrt(t+9))) ?
The first derivative of sin(t/(sqrt(t+9))) is (cos(t/(sqrt(t+9)))(t+18))/(2(t+9)sqrt(t+9))