What is the derivative of {f}(xsin(x)) ?

The derivative of {f}(xsin(x)) is derivative of {f}(x)sin(x)+cos(x){f}(x)

What is the first derivative of {f}(xsin(x)) ?

The first derivative of {f}(xsin(x)) is derivative of {f}(x)sin(x)+cos(x){f}(x)

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\frac{d}{d x} (f (x) sin (x))

\frac{d}{d x} (f (x)) sin (x) + cos (x) f (x)

Solution steps

\frac{d}{d x} (f (x) sin (x))

Apply the Product Rule:

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

f = f (x), g = sin (x)

= \frac{d}{d x} (f (x)) sin (x) + \frac{d}{d x} (sin (x)) f (x)

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

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

x \to 0 lim (\frac{x}{8 x ^{2} - x})

\frac{d}{d x} (\frac{x - a}{1 + x})

f (x) = 2 (x)^{4}

f (x) = ln (3 x + 2)

\frac{24}{x ^{2} + 12}

What is the derivative of {f}(xsin(x)) ?
The derivative of {f}(xsin(x)) is derivative of {f}(x)sin(x)+cos(x){f}(x)
What is the first derivative of {f}(xsin(x)) ?
The first derivative of {f}(xsin(x)) is derivative of {f}(x)sin(x)+cos(x){f}(x)