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Popular >

derivative of xln|cos(x|)

Solution

\frac{d}{d x} (x ln ∣ cos (x) ∣)

Solution

ln ∣ cos (x) ∣ - x tan (x)

Solution steps

\frac{d}{d x} (x ln ∣ cos (x) ∣)

Apply the Product Rule:

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

f = x, g = ln ∣ cos (x) ∣

= \frac{d x}{d x} ln ∣ cos (x) ∣ + \frac{d}{d x} (ln ∣ cos (x) ∣) x

\frac{d x}{d x} = 1

\frac{d}{d x} (ln ∣ cos (x) ∣) = - tan (x)

= 1 \cdot ln ∣ cos (x) ∣ + (- tan (x)) x

Simplify

= ln ∣ cos (x) ∣ - x tan (x)

Popular Examples

integral of (sin(8x))/8

\int \frac{sin ( 8 x )}{8} d x

integral of (13)/((1-x^2)^{3/2)}

\int \frac{13}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

(dy)/(dx)=ye^{-x^2},y(4)=1

\frac{d y}{d x} = y e^{- x^{2}}, y (4) = 1

y^2(dy)/(dx)=3x^2y^3-6x^2

y^{2} \frac{d y}{d x} = 3 x^{2} y^{3} - 6 x^{2}

(2dx)/(dt)+3x=0,x(0)=5

\frac{2 d x}{d t} + 3 x = 0, x (0) = 5

Frequently Asked Questions (FAQ)

What is the derivative of xln|cos(x|) ?
The derivative of xln|cos(x|) is ln|cos(x)|-xtan(x)
What is the first derivative of xln|cos(x|) ?
The first derivative of xln|cos(x|) is ln|cos(x)|-xtan(x)