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

The derivative of 5e^x(cos(x-sin(x))) is -10e^xsin(x)

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

The first derivative of 5e^x(cos(x-sin(x))) is -10e^xsin(x)

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

- 10 e^{x} sin (x)

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

5 (e^{x} (cos (x) - sin (x)) + (- sin (x) - cos (x)) e^{x}) : - 10 e^{x} sin (x)

= - 10 e^{x} sin (x)

\frac{d y}{d x} = (x - 8) e^{- 2 y}, y (8) = ln (8)

\frac{d}{d x} (tan^{4} (x))

\frac{d y}{d x} = (x 1 - y^{2})

\int 3 tan^{3} (θ) d θ

y^{^{'}} = x y^{2} (1 + x^{2})^{- \frac{1}{2}}, y (0) = 2

What is the derivative of 5e^x(cos(x-sin(x))) ?
The derivative of 5e^x(cos(x-sin(x))) is -10e^xsin(x)
What is the first derivative of 5e^x(cos(x-sin(x))) ?
The first derivative of 5e^x(cos(x-sin(x))) is -10e^xsin(x)