What is the derivative of sin(x/2-e^{-x^3}) ?

The derivative of sin(x/2-e^{-x^3}) is 1/2 cos(x/2)+3e^{-x^3}x^2

What is the first derivative of sin(x/2-e^{-x^3}) ?

The first derivative of sin(x/2-e^{-x^3}) is 1/2 cos(x/2)+3e^{-x^3}x^2

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\frac{d}{d x} (sin (\frac{x}{2}) - e^{- x^{3}})

\frac{1}{2} cos (\frac{x}{2}) + 3 e^{- x^{3}} x^{2}

Solution steps

\frac{d}{d x} (sin (\frac{x}{2}) - e^{- x^{3}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (sin (\frac{x}{2})) - \frac{d}{d x} (e^{- x^{3}})

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

\frac{d}{d x} (e^{- x^{3}}) = - 3 e^{- x^{3}} x^{2}

= cos (\frac{x}{2}) \frac{1}{2} - (- 3 e^{- x^{3}} x^{2})

Simplify

= \frac{1}{2} cos (\frac{x}{2}) + 3 e^{- x^{3}} x^{2}

\frac{\partial}{\partial x} ((\frac{y}{x - y})^{6})

x^{4^{x}}

\int 2 y^{2} cos (9 y) d y

y^{5} + 3 x^{2} y^{2} + 5 x^{4} = 49, (- 1, 2)

What is the derivative of sin(x/2-e^{-x^3}) ?
The derivative of sin(x/2-e^{-x^3}) is 1/2 cos(x/2)+3e^{-x^3}x^2
What is the first derivative of sin(x/2-e^{-x^3}) ?
The first derivative of sin(x/2-e^{-x^3}) is 1/2 cos(x/2)+3e^{-x^3}x^2