What is the derivative of 6e^x(cos(x-sin(x))) ?

The derivative of 6e^x(cos(x-sin(x))) is -12e^xsin(x)

What is the first derivative of 6e^x(cos(x-sin(x))) ?

The first derivative of 6e^x(cos(x-sin(x))) is -12e^xsin(x)

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Popular >

\frac{d}{d x} (6 e^{x} (cos (x) - sin (x)))

- 12 e^{x} sin (x)

Solution steps

\frac{d}{d x} (6 e^{x} (cos (x) - sin (x)))

Take the constant out:

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

= 6 \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)

= 6 (\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)

= 6 (e^{x} (cos (x) - sin (x)) + (- sin (x) - cos (x)) e^{x})

Simplify

6 (e^{x} (cos (x) - sin (x)) + (- sin (x) - cos (x)) e^{x}) : - 12 e^{x} sin (x)

= - 12 e^{x} sin (x)

\int 8 t^{3} d t

\frac{d}{d x} (\frac{1}{x})

x \to 1 + lim (\frac{x ^{2}}{∣ 1 - x ∣})

\int_{0}^{π} cos (θ) d θ

\frac{d}{d a} (a^{5} + a^{2} b^{3} - a^{3} b^{2} - b^{5})

What is the derivative of 6e^x(cos(x-sin(x))) ?
The derivative of 6e^x(cos(x-sin(x))) is -12e^xsin(x)
What is the first derivative of 6e^x(cos(x-sin(x))) ?
The first derivative of 6e^x(cos(x-sin(x))) is -12e^xsin(x)