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

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

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

The first derivative of {f}(x(sin(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)

\int \frac{1}{9 + 16 x ^{2}} d x

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

\int_{0}^{\infty} e^{- x} d x

\int x cos (x^{2}) d x

f (x) = 9 + \frac{3}{x}

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