What is the derivative of 5e^x(cos(x-x)) ?

The derivative of 5e^x(cos(x-x)) is 5(e^x(cos(x)-x)+(-sin(x)-1)e^x)

What is the first derivative of 5e^x(cos(x-x)) ?

The first derivative of 5e^x(cos(x-x)) is 5(e^x(cos(x)-x)+(-sin(x)-1)e^x)

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

5 (e^{x} (cos (x) - x) + (- sin (x) - 1) e^{x})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = e^{x}, g = cos (x) - x

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

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

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

= 5 (e^{x} (cos (x) - x) + (- sin (x) - 1) e^{x})

What is the derivative of 5e^x(cos(x-x)) ?
The derivative of 5e^x(cos(x-x)) is 5(e^x(cos(x)-x)+(-sin(x)-1)e^x)
What is the first derivative of 5e^x(cos(x-x)) ?
The first derivative of 5e^x(cos(x-x)) is 5(e^x(cos(x)-x)+(-sin(x)-1)e^x)