What is the derivative of (2x+1^2sec(x^3)) ?

The derivative of (2x+1^2sec(x^3)) is 4(2x+1)sec(x^3)+sec(x^3)tan(x^3)*3x^2(2x+1)^2

What is the first derivative of (2x+1^2sec(x^3)) ?

The first derivative of (2x+1^2sec(x^3)) is 4(2x+1)sec(x^3)+sec(x^3)tan(x^3)*3x^2(2x+1)^2

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

4 (2 x + 1) sec (x^{3}) + sec (x^{3}) tan (x^{3}) \cdot 3 x^{2} (2 x + 1)^{2}

Solution steps

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

Apply the Product Rule:

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

f = (2 x + 1)^{2}, g = sec (x^{3})

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

\frac{d}{d x} ((2 x + 1)^{2}) = 4 (2 x + 1)

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

= 4 (2 x + 1) sec (x^{3}) + sec (x^{3}) tan (x^{3}) \cdot 3 x^{2} (2 x + 1)^{2}

\int \frac{e ^{u}}{( 5 - e ^{u} ) ^{2}} d u

\int \frac{x ^{2} - 25}{x ^{3}} d x

t^{2} y^{^{''}} + 15 t y^{^{'}} + 49 y = 0

f (x) = cot (x) csc (x)

x \to \infty lim (8 ln (x))

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