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

The derivative of f(x)=(5x^2-7x)e^x is 5e^xx^2+3e^xx-7e^x

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

The first derivative of f(x)=(5x^2-7x)e^x is 5e^xx^2+3e^xx-7e^x

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derivative of

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

5 e^{x} x^{2} + 3 e^{x} x - 7 e^{x}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (5 x^{2} - 7 x) = 10 x - 7

\frac{d}{d x} (e^{x}) = e^{x}

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

Simplify

(10 x - 7) e^{x} + e^{x} (5 x^{2} - 7 x) : 5 e^{x} x^{2} + 3 e^{x} x - 7 e^{x}

= 5 e^{x} x^{2} + 3 e^{x} x - 7 e^{x}

\frac{d}{d x} (2^{s i n (π x)})

\int cos (x) sin (t - x) d x

\int_{- π}^{π} sin (2 x) sin (2 x) d x

y^{^{''}} - 7 y^{^{'}} + 14 y = - 784 t^{2}

y^{^{''}} + 9 y = 3 tan (3 x)

What is the derivative of f(x)=(5x^2-7x)e^x ?
The derivative of f(x)=(5x^2-7x)e^x is 5e^xx^2+3e^xx-7e^x
What is the first derivative of f(x)=(5x^2-7x)e^x ?
The first derivative of f(x)=(5x^2-7x)e^x is 5e^xx^2+3e^xx-7e^x