What is the derivative of \sqrt[4]{2x^{12}+sin(4x)} ?

The derivative of \sqrt[4]{2x^{12}+sin(4x)} is (6x^{11}+cos(4x))/((2x^{12)+sin(4x))^{3/4}}

What is the first derivative of \sqrt[4]{2x^{12}+sin(4x)} ?

The first derivative of \sqrt[4]{2x^{12}+sin(4x)} is (6x^{11}+cos(4x))/((2x^{12)+sin(4x))^{3/4}}

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derivative of

4 2 x^{12} + sin (4 x)

\frac{6 x ^{11} + cos ( 4 x )}{( 2 x ^{12} + sin ( 4 x ) ) ^{\frac{3}{4}}}

Solution steps

\frac{d}{d x} (4 2 x^{12} + sin (4 x))

Apply the chain rule:

\frac{1}{4 ( 2 x ^{12} + sin ( 4 x ) ) ^{\frac{3}{4}}} \frac{d}{d x} (2 x^{12} + sin (4 x))

= \frac{1}{4 ( 2 x ^{12} + sin ( 4 x ) ) ^{\frac{3}{4}}} \frac{d}{d x} (2 x^{12} + sin (4 x))

\frac{d}{d x} (2 x^{12} + sin (4 x)) = 24 x^{11} + cos (4 x) \cdot 4

= \frac{1}{4 ( 2 x ^{12} + sin ( 4 x ) ) ^{\frac{3}{4}}} (24 x^{11} + cos (4 x) \cdot 4)

Simplify

\frac{1}{4 ( 2 x ^{12} + sin ( 4 x ) ) ^{\frac{3}{4}}} (24 x^{11} + cos (4 x) \cdot 4) : \frac{6 x ^{11} + cos ( 4 x )}{( 2 x ^{12} + sin ( 4 x ) ) ^{\frac{3}{4}}}

= \frac{6 x ^{11} + cos ( 4 x )}{( 2 x ^{12} + sin ( 4 x ) ) ^{\frac{3}{4}}}

\frac{d}{d x} (- \frac{12 x}{( x ^{2} + 3 ) ^{2}})

\frac{\partial}{\partial x} (\frac{x y}{x ^{2} + 9})

\int 8 36 - 4 x - 32 d x

\int \frac{4 + 5 x}{1 + x ^{2}} d x

\frac{d}{d t} ((90 cos (\frac{π}{6})) t)

What is the derivative of \sqrt[4]{2x^{12}+sin(4x)} ?
The derivative of \sqrt[4]{2x^{12}+sin(4x)} is (6x^{11}+cos(4x))/((2x^{12)+sin(4x))^{3/4}}
What is the first derivative of \sqrt[4]{2x^{12}+sin(4x)} ?
The first derivative of \sqrt[4]{2x^{12}+sin(4x)} is (6x^{11}+cos(4x))/((2x^{12)+sin(4x))^{3/4}}