What is the derivative of f(x)=4x(sin(x)+cos(x)) ?

The derivative of f(x)=4x(sin(x)+cos(x)) is 4(sin(x)+cos(x)+x(cos(x)-sin(x)))

What is the first derivative of f(x)=4x(sin(x)+cos(x)) ?

The first derivative of f(x)=4x(sin(x)+cos(x)) is 4(sin(x)+cos(x)+x(cos(x)-sin(x)))

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derivative of

f (x) = 4 x (sin (x) + cos (x))

4 (sin (x) + cos (x) + x (cos (x) - sin (x)))

Solution steps

\frac{d}{d x} (4 x (sin (x) + cos (x)))

Take the constant out:

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

= 4 \frac{d}{d x} (x (sin (x) + cos (x)))

Apply the Product Rule:

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

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

= 4 (\frac{d x}{d x} (sin (x) + cos (x)) + \frac{d}{d x} (sin (x) + cos (x)) x)

\frac{d x}{d x} = 1

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

= 4 (1 \cdot (sin (x) + cos (x)) + (cos (x) - sin (x)) x)

Simplify

= 4 (sin (x) + cos (x) + x (cos (x) - sin (x)))

\int \frac{4 x + 5}{4 x + 6} d x

\frac{d}{d x} (\frac{e ^{- x}}{x ^{2}})

\int 8 t^{3} (1 + t^{4})^{10} d t

\int \frac{- 1}{x ( ln ( x ) ) ^{2}} d x

x^{2} + y^{2} = 17, (4, - 1)

What is the derivative of f(x)=4x(sin(x)+cos(x)) ?
The derivative of f(x)=4x(sin(x)+cos(x)) is 4(sin(x)+cos(x)+x(cos(x)-sin(x)))
What is the first derivative of f(x)=4x(sin(x)+cos(x)) ?
The first derivative of f(x)=4x(sin(x)+cos(x)) is 4(sin(x)+cos(x)+x(cos(x)-sin(x)))