What is the derivative of y=\sqrt[4]{(cos(x))^3} ?

The derivative of y=\sqrt[4]{(cos(x))^3} is -(3cos^2(x)sin(x))/(4(cos^3(x))^{3/4)}

What is the first derivative of y=\sqrt[4]{(cos(x))^3} ?

The first derivative of y=\sqrt[4]{(cos(x))^3} is -(3cos^2(x)sin(x))/(4(cos^3(x))^{3/4)}

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derivative of

- \frac{3 cos ^{2} ( x ) sin ( x )}{4 ( cos ^{3} ( x ) ) ^{\frac{3}{4}}}

Solution steps

Apply the chain rule:

\frac{1}{4 ( ( cos ( x ) ) ^{3} ) ^{\frac{3}{4}}} \frac{d}{d x} ((cos (x))^{3})

= \frac{1}{4 ( ( cos ( x ) ) ^{3} ) ^{\frac{3}{4}}} \frac{d}{d x} ((cos (x))^{3})

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

= \frac{1}{4 ( ( cos ( x ) ) ^{3} ) ^{\frac{3}{4}}} (- 3 cos^{2} (x) sin (x))

Simplify

\frac{1}{4 ( cos ^{3} ( x ) ) ^{\frac{3}{4}}} (- 3 cos^{2} (x) sin (x)) : - \frac{3 cos ^{2} ( x ) sin ( x )}{4 ( cos ^{3} ( x ) ) ^{\frac{3}{4}}}

= - \frac{3 cos ^{2} ( x ) sin ( x )}{4 ( cos ^{3} ( x ) ) ^{\frac{3}{4}}}

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

f (x) = a^{4} + cos^{4} (x)

\int_{0}^{1} 2 π (2 - y) (4 y^{2}) d y

\int - sin (d) x d x

What is the derivative of y=\sqrt[4]{(cos(x))^3} ?
The derivative of y=\sqrt[4]{(cos(x))^3} is -(3cos^2(x)sin(x))/(4(cos^3(x))^{3/4)}
What is the first derivative of y=\sqrt[4]{(cos(x))^3} ?
The first derivative of y=\sqrt[4]{(cos(x))^3} is -(3cos^2(x)sin(x))/(4(cos^3(x))^{3/4)}