What is the derivative of e^{ln(cos(x^2)}sqrt(2x+1)) ?

The derivative of e^{ln(cos(x^2)}sqrt(2x+1)) is -2xsin(x^2)sqrt(2x+1)+(cos(x^2))/(sqrt(2x+1))

What is the first derivative of e^{ln(cos(x^2)}sqrt(2x+1)) ?

The first derivative of e^{ln(cos(x^2)}sqrt(2x+1)) is -2xsin(x^2)sqrt(2x+1)+(cos(x^2))/(sqrt(2x+1))

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\frac{d}{d x} (e^{l n (c o s (x^{2}))} 2 x + 1)

- 2 x sin (x^{2}) 2 x + 1 + \frac{cos ( x ^{2} )}{2 x + 1}

Solution steps

\frac{d}{d x} (e^{l n (c o s (x^{2}))} 2 x + 1)

Simplify

e^{l n (c o s (x^{2}))} 2 x + 1 : cos (x^{2}) 2 x + 1

= \frac{d}{d x} (cos (x^{2}) 2 x + 1)

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (x^{2}), g = 2 x + 1

= \frac{d}{d x} (cos (x^{2})) 2 x + 1 + \frac{d}{d x} (2 x + 1) cos (x^{2})

\frac{d}{d x} (cos (x^{2})) = - sin (x^{2}) \cdot 2 x

\frac{d}{d x} (2 x + 1) = \frac{1}{2 x + 1}

= (- sin (x^{2}) \cdot 2 x) 2 x + 1 + \frac{1}{2 x + 1} cos (x^{2})

Simplify

(- sin (x^{2}) \cdot 2 x) 2 x + 1 + \frac{1}{2 x + 1} cos (x^{2}) : - 2 x sin (x^{2}) 2 x + 1 + \frac{cos ( x ^{2} )}{2 x + 1}

= - 2 x sin (x^{2}) 2 x + 1 + \frac{cos ( x ^{2} )}{2 x + 1}

\frac{d y}{d x} + 2 x y = 5 x

(- 4, - 6), (- 2, 0)

n = 1 \sum \infty n^{5} (1 + n^{6})^{6}

\frac{d}{d x} (\frac{f ( x )}{x ^{5}})

(5 x + 2)^{4} (2 x - 3)^{8}

What is the derivative of e^{ln(cos(x^2)}sqrt(2x+1)) ?
The derivative of e^{ln(cos(x^2)}sqrt(2x+1)) is -2xsin(x^2)sqrt(2x+1)+(cos(x^2))/(sqrt(2x+1))
What is the first derivative of e^{ln(cos(x^2)}sqrt(2x+1)) ?
The first derivative of e^{ln(cos(x^2)}sqrt(2x+1)) is -2xsin(x^2)sqrt(2x+1)+(cos(x^2))/(sqrt(2x+1))