What is the derivative of 7x(sin(x+cos(x))) ?

The derivative of 7x(sin(x+cos(x))) is 7(sin(x)+cos(x)+x(cos(x)-sin(x)))

What is the first derivative of 7x(sin(x+cos(x))) ?

The first derivative of 7x(sin(x+cos(x))) is 7(sin(x)+cos(x)+x(cos(x)-sin(x)))

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\frac{d}{d x} (7 x (sin (x) + cos (x)))

7 (sin (x) + cos (x) + x (cos (x) - sin (x)))

Solution steps

\frac{d}{d x} (7 x (sin (x) + cos (x)))

Take the constant out:

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

= 7 \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)

= 7 (\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)

= 7 (1 \cdot (sin (x) + cos (x)) + (cos (x) - sin (x)) x)

Simplify

= 7 (sin (x) + cos (x) + x (cos (x) - sin (x)))

\frac{d x}{d t} = 2 e^{t} - 2

(- 1.2) (4)

\int \frac{x}{( x + 1 ) ^{3}} d x

10 z^{2} e^{z}

What is the derivative of 7x(sin(x+cos(x))) ?
The derivative of 7x(sin(x+cos(x))) is 7(sin(x)+cos(x)+x(cos(x)-sin(x)))
What is the first derivative of 7x(sin(x+cos(x))) ?
The first derivative of 7x(sin(x+cos(x))) is 7(sin(x)+cos(x)+x(cos(x)-sin(x)))