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# Find the derivative of $\sin\left(x\right)\left(\sin\left(x\right)+\cos\left(x\right)\right)$

## Step-by-step Solution

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###  Videos

$\frac{2\sin\left(2x\right)+2\cos\left(x\right)^2-2\sin\left(x\right)^2}{2}$
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##  Step-by-step Solution 

Problem to solve:

$\frac{d}{dx}\left(\sin\left(x\right)\left(\sin\left(x\right)+\cos\left(x\right)\right)\right)$

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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\sin\left(x\right)$ and $g=\sin\left(x\right)+\cos\left(x\right)$

$\frac{d}{dx}\left(\sin\left(x\right)\right)\left(\sin\left(x\right)+\cos\left(x\right)\right)+\sin\left(x\right)\frac{d}{dx}\left(\sin\left(x\right)+\cos\left(x\right)\right)$

Learn how to solve differential calculus problems step by step online.

$\frac{d}{dx}\left(\sin\left(x\right)\right)\left(\sin\left(x\right)+\cos\left(x\right)\right)+\sin\left(x\right)\frac{d}{dx}\left(\sin\left(x\right)+\cos\left(x\right)\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative of sin(x)(sin(x)+cos(x)). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\sin\left(x\right) and g=\sin\left(x\right)+\cos\left(x\right). The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}.

$\frac{2\sin\left(2x\right)+2\cos\left(x\right)^2-2\sin\left(x\right)^2}{2}$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Find the derivativeFind d/dx(sin(x)(sin(x)+cos(x))) using the product ruleFind d/dx(sin(x)(sin(x)+cos(x))) using the quotient ruleFind d/dx(sin(x)(sin(x)+cos(x))) using logarithmic differentiation

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v
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x
y
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.
(◻)
+
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◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### Main topic:

Differential Calculus

~ 0.14 s

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