What is the derivative of (1+sin(x)cos(x)) ?

The derivative of (1+sin(x)cos(x)) is cos^2(x)-sin(x)(1+sin(x))

What is the first derivative of (1+sin(x)cos(x)) ?

The first derivative of (1+sin(x)cos(x)) is cos^2(x)-sin(x)(1+sin(x))

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\frac{d}{d x} ((1 + sin (x)) cos (x))

cos^{2} (x) - sin (x) (1 + sin (x))

Solution steps

\frac{d}{d x} ((1 + sin (x)) cos (x))

Apply the Product Rule:

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

f = 1 + sin (x), g = cos (x)

= \frac{d}{d x} (1 + sin (x)) cos (x) + \frac{d}{d x} (cos (x)) (1 + sin (x))

\frac{d}{d x} (1 + sin (x)) = cos (x)

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

= cos (x) cos (x) + (- sin (x)) (1 + sin (x))

Simplify

cos (x) cos (x) + (- sin (x)) (1 + sin (x)) : cos^{2} (x) - sin (x) (1 + sin (x))

= cos^{2} (x) - sin (x) (1 + sin (x))

\frac{\partial}{\partial y} (3 x^{2} - 3)

\int \frac{7 x ^{6} + 6}{x ^{7} + 6 x} d x

\int e^{10 x} - 9 d x

n = 3 \sum \infty \frac{2}{5 ^{n}}

x \to 0 + lim (x + ∣ x ∣)

What is the derivative of (1+sin(x)cos(x)) ?
The derivative of (1+sin(x)cos(x)) is cos^2(x)-sin(x)(1+sin(x))
What is the first derivative of (1+sin(x)cos(x)) ?
The first derivative of (1+sin(x)cos(x)) is cos^2(x)-sin(x)(1+sin(x))