What is the derivative of tan(x+cos^2(x)+sin^2(x)-3) ?

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

What is the first derivative of tan(x+cos^2(x)+sin^2(x)-3) ?

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

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\frac{d}{d x} (tan (x) + cos^{2} (x) + sin^{2} (x) - 3)

sec^{2} (x)

Solution steps

\frac{d}{d x} (tan (x) + cos^{2} (x) + sin^{2} (x) - 3)

Simplify

tan (x) + cos^{2} (x) + sin^{2} (x) - 3 : tan (x) - 2

= \frac{d}{d x} (tan (x) - 2)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (tan (x)) - \frac{d}{d x} (2)

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

\frac{d}{d x} (2) = 0

= sec^{2} (x) - 0

Simplify

= sec^{2} (x)

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