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Find the derivative of $x\cos\left(x^2-1\right)$

Step-by-step Solution

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Final Answer

$\cos\left(x^2-1\right)-2x\cdot x\sin\left(x^2-1\right)$
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Step-by-step Solution

Problem to solve:

$\frac{d}{dx}\left(x\cos\left(x^2-1\right)\right)$

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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=\cos\left(x^2-1\right)$

$\frac{d}{dx}\left(x\right)\cos\left(x^2-1\right)+x\frac{d}{dx}\left(\cos\left(x^2-1\right)\right)$

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

$\frac{d}{dx}\left(x\right)\cos\left(x^2-1\right)+x\frac{d}{dx}\left(\cos\left(x^2-1\right)\right)$

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Learn how to solve differential calculus problems step by step online. Find the derivative of xcos(x^2-1). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\cos\left(x^2-1\right). The derivative of the linear function is equal to 1. The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x). The derivative of a sum of two or more functions is the sum of the derivatives of each function.

Final Answer

$\cos\left(x^2-1\right)-2x\cdot x\sin\left(x^2-1\right)$

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 derivative of xcos(x^2-1) using the product ruleFind derivative of xcos(x^2-1) using the quotient ruleFind derivative of xcos(x^2-1) using logarithmic differentiationFind derivative of xcos(x^2-1) using the definition

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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

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