👉 Try now NerdPal! Our new math app on iOS and Android

Find the derivative of $\frac{d}{dx}\left(\sin\left(x\right)\left(\sin\left(x\right)+\cos\left(x\right)\right)\right)$

Step-by-step Solution

Go!
Math mode
Text mode
Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
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

Final Answer

$\frac{2\sin\left(2x\right)+2\cos\left(x\right)^2-2\sin\left(x\right)^2}{2}$
Got another answer? Verify it here!

Step-by-step Solution

Specify the solving method

1

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.

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

Unlock unlimited step-by-step solutions and much more!

Create a free account and unlock a glimpse of this solution.

Learn how to solve differential calculus problems step by step online. Find the derivative of d/dx(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)}.

Final Answer

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

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 derivative of sinx(sinx+cosx) using the product ruleFind derivative of sinx(sinx+cosx) using the quotient ruleFind derivative of sinx(sinx+cosx) using logarithmic differentiation

Give us your feedback!

Function Plot

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

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
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

How to improve your answer:

Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

Used Formulas

4. See formulas

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

Unlimited step-by-step math solutions. No ads.

Includes multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android apps as well.

20% discount on online tutoring.

Choose your subscription plan:
Have a promo code?
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account