What is the derivative of f(x)=sin(x)-1/3 sin(3x)+1/5 sin(5x) ?

The derivative of f(x)=sin(x)-1/3 sin(3x)+1/5 sin(5x) is cos(x)-cos(3x)+cos(5x)

What is the first derivative of f(x)=sin(x)-1/3 sin(3x)+1/5 sin(5x) ?

The first derivative of f(x)=sin(x)-1/3 sin(3x)+1/5 sin(5x) is cos(x)-cos(3x)+cos(5x)

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derivative of

f (x) = sin (x) - \frac{1}{3} sin (3 x) + \frac{1}{5} sin (5 x)

cos (x) - cos (3 x) + cos (5 x)

Solution steps

\frac{d}{d x} (sin (x) - \frac{1}{3} sin (3 x) + \frac{1}{5} sin (5 x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (sin (x)) - \frac{d}{d x} (\frac{1}{3} sin (3 x)) + \frac{d}{d x} (\frac{1}{5} sin (5 x))

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

\frac{d}{d x} (\frac{1}{3} sin (3 x)) = cos (3 x)

\frac{d}{d x} (\frac{1}{5} sin (5 x)) = cos (5 x)

= cos (x) - cos (3 x) + cos (5 x)

\int 1 - e^{- x^{2}} d x

sin (y)

\int \frac{1}{x ( x + 4 )} d x

\int x \cdot 9^{2 x^{2} - 8} d x

\int x 3 4 + x^{2} d x

What is the derivative of f(x)=sin(x)-1/3 sin(3x)+1/5 sin(5x) ?
The derivative of f(x)=sin(x)-1/3 sin(3x)+1/5 sin(5x) is cos(x)-cos(3x)+cos(5x)
What is the first derivative of f(x)=sin(x)-1/3 sin(3x)+1/5 sin(5x) ?
The first derivative of f(x)=sin(x)-1/3 sin(3x)+1/5 sin(5x) is cos(x)-cos(3x)+cos(5x)