What is the derivative of f(x)=4e^{5x^2}(5-x)^7 ?

The derivative of f(x)=4e^{5x^2}(5-x)^7 is 4(10e^{5x^2}x(5-x)^7-7e^{5x^2}(5-x)^6)

What is the first derivative of f(x)=4e^{5x^2}(5-x)^7 ?

The first derivative of f(x)=4e^{5x^2}(5-x)^7 is 4(10e^{5x^2}x(5-x)^7-7e^{5x^2}(5-x)^6)

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derivative of

f (x) = 4 e^{5 x^{2}} (5 - x)^{7}

4 (10 e^{5 x^{2}} x (5 - x)^{7} - 7 e^{5 x^{2}} (5 - x)^{6})

Solution steps

\frac{d}{d x} (4 e^{5 x^{2}} (5 - x)^{7})

Take the constant out:

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

= 4 \frac{d}{d x} (e^{5 x^{2}} (5 - x)^{7})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{5 x^{2}}, g = (5 - x)^{7}

= 4 (\frac{d}{d x} (e^{5 x^{2}}) (5 - x)^{7} + \frac{d}{d x} ((5 - x)^{7}) e^{5 x^{2}})

\frac{d}{d x} (e^{5 x^{2}}) = e^{5 x^{2}} \cdot 10 x

\frac{d}{d x} ((5 - x)^{7}) = - 7 (5 - x)^{6}

= 4 (e^{5 x^{2}} \cdot 10 x (5 - x)^{7} + (- 7 (5 - x)^{6}) e^{5 x^{2}})

Simplify

= 4 (10 e^{5 x^{2}} x (5 - x)^{7} - 7 e^{5 x^{2}} (5 - x)^{6})

\frac{\partial}{\partial x} ((x + y) e^{y^{2}})

\int (sin (x^{2})) d x

\frac{\partial}{\partial x} (9 + x^{2} + y^{2})

\frac{d ^{2}}{d x ^{2}} (\frac{10}{3 x ^{3}})

\frac{\partial}{\partial x} (x^{2} - x y^{2} + 4 y^{5})

What is the derivative of f(x)=4e^{5x^2}(5-x)^7 ?
The derivative of f(x)=4e^{5x^2}(5-x)^7 is 4(10e^{5x^2}x(5-x)^7-7e^{5x^2}(5-x)^6)
What is the first derivative of f(x)=4e^{5x^2}(5-x)^7 ?
The first derivative of f(x)=4e^{5x^2}(5-x)^7 is 4(10e^{5x^2}x(5-x)^7-7e^{5x^2}(5-x)^6)