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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derivative of

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_{7}^{14} 196 - x^{2} d x

\int \frac{1}{3} e^{x + 3} + \frac{3}{x} - 5 d x

y^{^{'}} = \frac{y ^{2}}{x y + y ^{2}}

\frac{2 t}{2 + t}

t (\frac{d y}{d t}) + 34 y = \frac{1}{t}

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)