What is the derivative of (5+3xsin(x)) ?

The derivative of (5+3xsin(x)) is 3sin(x)+cos(x)(5+3x)

What is the first derivative of (5+3xsin(x)) ?

The first derivative of (5+3xsin(x)) is 3sin(x)+cos(x)(5+3x)

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

3 sin (x) + cos (x) (5 + 3 x)

Solution steps

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

Apply the Product Rule:

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

f = 5 + 3 x, g = sin (x)

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

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

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

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

(y^{4} x) (\frac{d y}{d x}) = 1 + x, y (1) = 15

\frac{d y}{d x} = 3 - 2 y

x \to 7 lim (\frac{6 + 3}{6 ( 6 )})

\int 4 e^{4 x} d x

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

What is the derivative of (5+3xsin(x)) ?
The derivative of (5+3xsin(x)) is 3sin(x)+cos(x)(5+3x)
What is the first derivative of (5+3xsin(x)) ?
The first derivative of (5+3xsin(x)) is 3sin(x)+cos(x)(5+3x)