What is the derivative of (1-tan^2(x))3(1-sec^2(x))4 ?

The derivative of (1-tan^2(x))3(1-sec^2(x))4 is -12(2sec^2(x)tan(x)-4tan^3(x)sec^2(x))

What is the first derivative of (1-tan^2(x))3(1-sec^2(x))4 ?

The first derivative of (1-tan^2(x))3(1-sec^2(x))4 is -12(2sec^2(x)tan(x)-4tan^3(x)sec^2(x))

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derivative of

(1 - tan^{2} (x)) 3 (1 - sec^{2} (x)) 4

- 12 (2 sec^{2} (x) tan (x) - 4 tan^{3} (x) sec^{2} (x))

Solution steps

\frac{d}{d x} ((1 - tan^{2} (x)) \cdot 3 (1 - sec^{2} (x)) \cdot 4)

Simplify

(1 - tan^{2} (x)) \cdot 3 (1 - sec^{2} (x)) \cdot 4 : - 12 tan^{2} (x) (1 - tan^{2} (x))

= \frac{d}{d x} (- 12 tan^{2} (x) (1 - tan^{2} (x)))

Take the constant out:

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

= - 12 \frac{d}{d x} (tan^{2} (x) (1 - tan^{2} (x)))

Apply the Product Rule:

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

f = tan^{2} (x), g = 1 - tan^{2} (x)

= - 12 (\frac{d}{d x} (tan^{2} (x)) (1 - tan^{2} (x)) + \frac{d}{d x} (1 - tan^{2} (x)) tan^{2} (x))

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

\frac{d}{d x} (1 - tan^{2} (x)) = - 2 sec^{2} (x) tan (x)

= - 12 (2 tan (x) sec^{2} (x) (1 - tan^{2} (x)) + (- 2 sec^{2} (x) tan (x)) tan^{2} (x))

Simplify

- 12 (2 tan (x) sec^{2} (x) (1 - tan^{2} (x)) + (- 2 sec^{2} (x) tan (x)) tan^{2} (x)) : - 12 (2 sec^{2} (x) tan (x) - 4 tan^{3} (x) sec^{2} (x))

= - 12 (2 sec^{2} (x) tan (x) - 4 tan^{3} (x) sec^{2} (x))

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

x^{3} - 2 x^{2} - 3

y = cos (lo g_{4} (x))

\frac{( 3 x - 1 )}{( 2 x + 1 )}

w \cdot r t x cos (3 x^{2} + 5)

What is the derivative of (1-tan^2(x))3(1-sec^2(x))4 ?
The derivative of (1-tan^2(x))3(1-sec^2(x))4 is -12(2sec^2(x)tan(x)-4tan^3(x)sec^2(x))
What is the first derivative of (1-tan^2(x))3(1-sec^2(x))4 ?
The first derivative of (1-tan^2(x))3(1-sec^2(x))4 is -12(2sec^2(x)tan(x)-4tan^3(x)sec^2(x))