What is the derivative of f(x)=7e^xcos(x) ?

The derivative of f(x)=7e^xcos(x) is 7(e^xcos(x)-e^xsin(x))

What is the first derivative of f(x)=7e^xcos(x) ?

The first derivative of f(x)=7e^xcos(x) is 7(e^xcos(x)-e^xsin(x))

derivative of

f (x) = 7 e^{x} cos (x)

7 (e^{x} cos (x) - e^{x} sin (x))

Solution steps

\frac{d}{d x} (7 e^{x} cos (x))

Take the constant out:

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

= 7 \frac{d}{d x} (e^{x} cos (x))

Apply the Product Rule:

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

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

= 7 (\frac{d}{d x} (e^{x}) cos (x) + \frac{d}{d x} (cos (x)) e^{x})

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

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

= 7 (e^{x} cos (x) + (- sin (x)) e^{x})

Simplify

= 7 (e^{x} cos (x) - e^{x} sin (x))

\int 6 cot^{4} (x) d x

y^{^{''}} - 4 y = e^{- 2 x} - 2 x, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + y = \frac{3}{2} sin (x)

\int x + 1 x d x

\int \frac{sin ( 2 x )}{18 + cos ^{2} ( x )} d x

What is the derivative of f(x)=7e^xcos(x) ?
The derivative of f(x)=7e^xcos(x) is 7(e^xcos(x)-e^xsin(x))
What is the first derivative of f(x)=7e^xcos(x) ?
The first derivative of f(x)=7e^xcos(x) is 7(e^xcos(x)-e^xsin(x))