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Popular >

derivative of 9excos(x)

Solution

derivative of

9 e x cos (x)

Solution

9 e (cos (x) - x sin (x))

Solution steps

\frac{d}{d x} (9 e x cos (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 9 e \frac{d}{d x} (x cos (x))

Apply the Product Rule:

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

f = x, g = cos (x)

= 9 e (\frac{d x}{d x} cos (x) + \frac{d}{d x} (cos (x)) x)

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

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

= 9 e (1 \cdot cos (x) + (- sin (x)) x)

Simplify

= 9 e (cos (x) - x sin (x))

Popular Examples

integral of (x^4)/(5x^5+4)

\int \frac{x ^{4}}{5 x ^{5} + 4} d x

derivative of 2e^{2e^x+x}

\frac{d}{d x} (2 e^{2 e^{x} + x})

integral of 1/(x^2sqrt(x^2-11))

\int \frac{1}{x ^{2} x ^{2} - 11} d x

derivative of e^{(ln(x)/x})

\frac{d}{d x} (e^{\frac{l n ( x )}{x}})

(dy)/(dx)=e^{9x-8y}

\frac{d y}{d x} = e^{9 x - 8 y}

Frequently Asked Questions (FAQ)

What is the derivative of 9excos(x) ?
The derivative of 9excos(x) is 9e(cos(x)-xsin(x))
What is the first derivative of 9excos(x) ?
The first derivative of 9excos(x) is 9e(cos(x)-xsin(x))