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Popular >

derivative of f(x)=sqrt(5+4e^{3x)}

Solution

derivative of

f (x) = 5 + 4 e^{3 x}

Solution

\frac{6 e ^{3 x}}{5 + 4 e ^{3 x}}

Solution steps

\frac{d}{d x} (5 + 4 e^{3 x})

Apply the chain rule:

\frac{1}{2 5 + 4 e ^{3 x}} \frac{d}{d x} (5 + 4 e^{3 x})

= \frac{1}{2 5 + 4 e ^{3 x}} \frac{d}{d x} (5 + 4 e^{3 x})

\frac{d}{d x} (5 + 4 e^{3 x}) = 12 e^{3 x}

= \frac{1}{2 5 + 4 e ^{3 x}} \cdot 12 e^{3 x}

Simplify

\frac{1}{2 5 + 4 e ^{3 x}} \cdot 12 e^{3 x} : \frac{6 e ^{3 x}}{5 + 4 e ^{3 x}}

= \frac{6 e ^{3 x}}{5 + 4 e ^{3 x}}

Popular Examples

y^{''}+16y^'+64y=0,y(0)=-3,y^'(0)=28

y^{^{''}} + 16 y^{^{'}} + 64 y = 0, y (0) = - 3, y^{^{'}} (0) = 28

integral from 0 to 8 of sqrt(1+81/4 x)

\int_{0}^{8} 1 + \frac{81}{4} x d x

derivative of 4x^2-6x+2 derivative of

4 x^{2} - 6 x + 2

derivative of 5sin(x(4/(x^3)+3x))

\frac{d}{d x} (5 sin (x) (\frac{4}{x ^{3}} + 3 x))

derivative of arccos(x+1)derivative of

arccos (x + 1)

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=sqrt(5+4e^{3x)} ?
The derivative of f(x)=sqrt(5+4e^{3x)} is (6e^{3x})/(sqrt(5+4e^{3x))}
What is the first derivative of f(x)=sqrt(5+4e^{3x)} ?
The first derivative of f(x)=sqrt(5+4e^{3x)} is (6e^{3x})/(sqrt(5+4e^{3x))}