What is the derivative of 5e^{-zx^2} ?

The derivative of 5e^{-zx^2} is -5e^{-zx^2}x^2

What is the first derivative of 5e^{-zx^2} ?

The first derivative of 5e^{-zx^2} is -5e^{-zx^2}x^2

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derivative of

5 e^{- z x^{2}}

- 5 e^{- z x^{2}} x^{2}

Solution steps

\frac{d}{d z} (5 e^{- z x^{2}})

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d z} (e^{- z x^{2}})

Apply the chain rule:

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

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

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

= 5 e^{- z x^{2}} (- x^{2})

Simplify

= - 5 e^{- z x^{2}} x^{2}

x \to 0 lim (\frac{x ^{5} + 2 x}{x})

\int \frac{3 x}{( x + 1 ) ^{2}} d x

y = \frac{1}{x - 6}, (- 3, - \frac{1}{9})

y^{^{'}} + 2 t y = 1

\int_{2}^{\infty} 7 x^{- 2} d x

What is the derivative of 5e^{-zx^2} ?
The derivative of 5e^{-zx^2} is -5e^{-zx^2}x^2
What is the first derivative of 5e^{-zx^2} ?
The first derivative of 5e^{-zx^2} is -5e^{-zx^2}x^2