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Find the derivative of $5e^{7x}\cos\left(9x\right)$

Step-by-step Solution

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Final Answer

$35e^{7x}\cos\left(9x\right)-45e^{7x}\sin\left(9x\right)$
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Step-by-step Solution

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

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

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

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

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Learn how to solve differential calculus problems step by step online. Find the derivative of 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.

Final Answer

$35e^{7x}\cos\left(9x\right)-45e^{7x}\sin\left(9x\right)$

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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 5e^7x using the product ruleFind derivative of 5e^7x using the quotient ruleFind derivative of 5e^7x using logarithmic differentiation

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Function Plot

Plotting: $35e^{7x}\cos\left(9x\right)-45e^{7x}\sin\left(9x\right)$

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5
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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

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

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