What is the derivative of cos^4(x+sec(x^3)) ?

The derivative of cos^4(x+sec(x^3)) is -4cos^3(x)sin(x)+sec(x^3)tan(x^3)*3x^2

What is the first derivative of cos^4(x+sec(x^3)) ?

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

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\frac{d}{d x} (cos^{4} (x) + sec (x^{3}))

- 4 cos^{3} (x) sin (x) + sec (x^{3}) tan (x^{3}) \cdot 3 x^{2}

Solution steps

\frac{d}{d x} (cos^{4} (x) + sec (x^{3}))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (cos^{4} (x)) + \frac{d}{d x} (sec (x^{3}))

\frac{d}{d x} (cos^{4} (x)) = - 4 cos^{3} (x) sin (x)

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

= - 4 cos^{3} (x) sin (x) + sec (x^{3}) tan (x^{3}) \cdot 3 x^{2}

\int cos (x) d x

\int \frac{1}{x ^{2} + z ^{2}} d x

f (x) = 4 x + 1

\frac{d y}{d t} - (\frac{3}{t}) y = 2 t^{3} e^{2 t}

\frac{\partial}{\partial x} (cos (5 x - 2 y^{2}))

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