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# Find the derivative using the quotient rule $\frac{d}{dx}\left(5e^{7x}\cos\left(9x\right)\right)$

## Step-by-step Solution

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###  Videos

$5e^{7x}\left(7\cos\left(9x\right)-9\sin\left(9x\right)\right)$
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## Step-by-step Solution

Problem to solve:

$\frac{d}{dx}\left(5\cdot e^{7x}\cdot \cos\left(9x\right)\right)$

Specify the solving method

1

The derivative of a function multiplied by a constant ($5$) is equal to the constant times the derivative of the function

$5\frac{d}{dx}\left(e^{7x}\cos\left(9x\right)\right)$
2

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=e^{7x}$ and $g=\cos\left(9x\right)$

$5\left(\frac{d}{dx}\left(e^{7x}\right)\cos\left(9x\right)+e^{7x}\frac{d}{dx}\left(\cos\left(9x\right)\right)\right)$

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

$5\frac{d}{dx}\left(e^{7x}\cos\left(9x\right)\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative using the quotient rule d/dx(5e^(7x)cos(9x)). The derivative of a function multiplied by a constant (5) is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=e^{7x} and g=\cos\left(9x\right). 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 the linear function times a constant, is equal to the constant.

$5e^{7x}\left(7\cos\left(9x\right)-9\sin\left(9x\right)\right)$

##  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 d/dx(5e^(7x)cos(9x)) using the product ruleFind d/dx(5e^(7x)cos(9x)) using logarithmic differentiation
SnapXam A2

### beta Got a different answer? Verify it!

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0
a
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n
u
v
w
x
y
z
.
(◻)
+
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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

$\frac{d}{dx}\left(5\cdot e^{7x}\cdot \cos\left(9x\right)\right)$