What is the derivative of f(x)=e^{7x}cos(10x) ?

The derivative of f(x)=e^{7x}cos(10x) is 7e^{7x}cos(10x)-10e^{7x}sin(10x)

What is the first derivative of f(x)=e^{7x}cos(10x) ?

The first derivative of f(x)=e^{7x}cos(10x) is 7e^{7x}cos(10x)-10e^{7x}sin(10x)

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derivative of

f (x) = e^{7 x} cos (10 x)

7 e^{7 x} cos (10 x) - 10 e^{7 x} sin (10 x)

Solution steps

\frac{d}{d x} (e^{7 x} cos (10 x))

Apply the Product Rule:

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

f = e^{7 x}, g = cos (10 x)

= \frac{d}{d x} (e^{7 x}) cos (10 x) + \frac{d}{d x} (cos (10 x)) e^{7 x}

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

\frac{d}{d x} (cos (10 x)) = - sin (10 x) \cdot 10

= e^{7 x} \cdot 7 cos (10 x) + (- sin (10 x) \cdot 10) e^{7 x}

Simplify

= 7 e^{7 x} cos (10 x) - 10 e^{7 x} sin (10 x)

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What is the derivative of f(x)=e^{7x}cos(10x) ?
The derivative of f(x)=e^{7x}cos(10x) is 7e^{7x}cos(10x)-10e^{7x}sin(10x)
What is the first derivative of f(x)=e^{7x}cos(10x) ?
The first derivative of f(x)=e^{7x}cos(10x) is 7e^{7x}cos(10x)-10e^{7x}sin(10x)