What is the derivative of sin(t/(sqrt(t+4))) ?

The derivative of sin(t/(sqrt(t+4))) is (cos(t/(sqrt(t+4)))(t+8))/(2(t+4)sqrt(t+4))

What is the first derivative of sin(t/(sqrt(t+4))) ?

The first derivative of sin(t/(sqrt(t+4))) is (cos(t/(sqrt(t+4)))(t+8))/(2(t+4)sqrt(t+4))

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derivative of

sin (\frac{t}{t + 4})

\frac{cos ( \frac{t}{t + 4} ) ( t + 8 )}{2 ( t + 4 ) t + 4}

Solution steps

\frac{d}{d t} (sin (\frac{t}{t + 4}))

Apply the chain rule:

cos (\frac{t}{t + 4}) \frac{d}{d t} (\frac{t}{t + 4})

= cos (\frac{t}{t + 4}) \frac{d}{d t} (\frac{t}{t + 4})

\frac{d}{d t} (\frac{t}{t + 4}) = \frac{t + 8}{2 ( t + 4 ) t + 4}

= cos (\frac{t}{t + 4}) \frac{t + 8}{2 ( t + 4 ) t + 4}

Multiply fractions:

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

= \frac{cos ( \frac{t}{t + 4} ) ( t + 8 )}{2 ( t + 4 ) t + 4}

x^{4} - 4 x^{3}

x \to 0 + lim (tan (\frac{1}{x}))

\frac{\partial}{\partial y} (ln (x y))

\int (3 y^{2} - 2 sin (y)) d y

(x - 2)^{2} (x - 3)^{3}

What is the derivative of sin(t/(sqrt(t+4))) ?
The derivative of sin(t/(sqrt(t+4))) is (cos(t/(sqrt(t+4)))(t+8))/(2(t+4)sqrt(t+4))
What is the first derivative of sin(t/(sqrt(t+4))) ?
The first derivative of sin(t/(sqrt(t+4))) is (cos(t/(sqrt(t+4)))(t+8))/(2(t+4)sqrt(t+4))