What is the derivative of sin(5x+tan(3x)) ?

The derivative of sin(5x+tan(3x)) is cos(5x)*5+sec^2(3x)*3

What is the first derivative of sin(5x+tan(3x)) ?

The first derivative of sin(5x+tan(3x)) is cos(5x)*5+sec^2(3x)*3

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

cos (5 x) \cdot 5 + sec^{2} (3 x) \cdot 3

Solution steps

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

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (sin (5 x)) + \frac{d}{d x} (tan (3 x))

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

\frac{d}{d x} (tan (3 x)) = sec^{2} (3 x) \cdot 3

= cos (5 x) \cdot 5 + sec^{2} (3 x) \cdot 3

What is the derivative of sin(5x+tan(3x)) ?
The derivative of sin(5x+tan(3x)) is cos(5x)*5+sec^2(3x)*3
What is the first derivative of sin(5x+tan(3x)) ?
The first derivative of sin(5x+tan(3x)) is cos(5x)*5+sec^2(3x)*3