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Popular >

derivative of sin(5x+cos(5x))

Solution

\frac{d}{d x} (sin (5 x) + cos (5 x))

Solution

cos (5 x) \cdot 5 - sin (5 x) \cdot 5

Solution steps

\frac{d}{d x} (sin (5 x) + cos (5 x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (sin (5 x)) + \frac{d}{d x} (cos (5 x))

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

\frac{d}{d x} (cos (5 x)) = - sin (5 x) \cdot 5

= cos (5 x) \cdot 5 - sin (5 x) \cdot 5

Popular Examples

limit as x approaches 2+of 4/((x-2)^3)

x \to 2 + lim (\frac{4}{( x - 2 ) ^{3}})

derivative of 3x^{1/3}+2x^2

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

integral of e^{3x}sin(e^x)

\int e^{3 x} sin (e^{x}) d x

derivative of sqrt(x)+1/(\sqrt[3]{x})

limit as x approaches-infinity of 2^x

x \to - \infty lim (2^{x})

Frequently Asked Questions (FAQ)

What is the derivative of sin(5x+cos(5x)) ?
The derivative of sin(5x+cos(5x)) is cos(5x)*5-sin(5x)*5
What is the first derivative of sin(5x+cos(5x)) ?
The first derivative of sin(5x+cos(5x)) is cos(5x)*5-sin(5x)*5