What is the derivative of 5(-csc^2(x+sec^2(x))) ?

The derivative of 5(-csc^2(x+sec^2(x))) is 5(2csc^2(x)cot(x)+2sec^2(x)tan(x))

What is the first derivative of 5(-csc^2(x+sec^2(x))) ?

The first derivative of 5(-csc^2(x+sec^2(x))) is 5(2csc^2(x)cot(x)+2sec^2(x)tan(x))

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\frac{d}{d x} (5 (- csc^{2} (x) + sec^{2} (x)))

5 (2 csc^{2} (x) cot (x) + 2 sec^{2} (x) tan (x))

Solution steps

\frac{d}{d x} (5 (- csc^{2} (x) + sec^{2} (x)))

Take the constant out:

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

= 5 \frac{d}{d x} (- csc^{2} (x) + sec^{2} (x))

Apply the Sum/Difference Rule:

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

= 5 (- \frac{d}{d x} (csc^{2} (x)) + \frac{d}{d x} (sec^{2} (x)))

\frac{d}{d x} (csc^{2} (x)) = - 2 csc^{2} (x) cot (x)

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

= 5 (- (- 2 csc^{2} (x) cot (x)) + 2 sec^{2} (x) tan (x))

Simplify

= 5 (2 csc^{2} (x) cot (x) + 2 sec^{2} (x) tan (x))

\int x csc (2 x) cot (2 x) d x

\int \frac{1}{( 25 + x ^{2} ) ^{2}} d x

f (x) = x^{2}, g (x) = 3 x

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

\frac{\partial}{\partial y} (x^{2} + 4 y^{2} - 800)

What is the derivative of 5(-csc^2(x+sec^2(x))) ?
The derivative of 5(-csc^2(x+sec^2(x))) is 5(2csc^2(x)cot(x)+2sec^2(x)tan(x))
What is the first derivative of 5(-csc^2(x+sec^2(x))) ?
The first derivative of 5(-csc^2(x+sec^2(x))) is 5(2csc^2(x)cot(x)+2sec^2(x)tan(x))