What is the derivative of f(x)=5x^2tan(1-sqrt(x)) ?

The derivative of f(x)=5x^2tan(1-sqrt(x)) is 5(2xtan(1-sqrt(x))-(x^{3/2}sec^2(-sqrt(x)+1))/2)

What is the first derivative of f(x)=5x^2tan(1-sqrt(x)) ?

The first derivative of f(x)=5x^2tan(1-sqrt(x)) is 5(2xtan(1-sqrt(x))-(x^{3/2}sec^2(-sqrt(x)+1))/2)

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derivative of

f (x) = 5 x^{2} tan (1 - x)

5 (2 x tan (1 - x) - \frac{x ^{\frac{3}{2}} sec ^{2} ( - x + 1 )}{2})

Solution steps

\frac{d}{d x} (5 x^{2} tan (1 - x))

Take the constant out:

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

= 5 \frac{d}{d x} (x^{2} tan (1 - x))

Apply the Product Rule:

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

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

= 5 (\frac{d}{d x} (x^{2}) tan (1 - x) + \frac{d}{d x} (tan (1 - x)) x^{2})

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

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

= 5 (2 x tan (1 - x) + (- \frac{sec ^{2} ( 1 - x )}{2 x}) x^{2})

Simplify

5 (2 x tan (1 - x) + (- \frac{sec ^{2} ( 1 - x )}{2 x}) x^{2}) : 5 (2 x tan (1 - x) - \frac{x ^{\frac{3}{2}} sec ^{2} ( - x + 1 )}{2})

= 5 (2 x tan (1 - x) - \frac{x ^{\frac{3}{2}} sec ^{2} ( - x + 1 )}{2})

What is the derivative of f(x)=5x^2tan(1-sqrt(x)) ?
The derivative of f(x)=5x^2tan(1-sqrt(x)) is 5(2xtan(1-sqrt(x))-(x^{3/2}sec^2(-sqrt(x)+1))/2)
What is the first derivative of f(x)=5x^2tan(1-sqrt(x)) ?
The first derivative of f(x)=5x^2tan(1-sqrt(x)) is 5(2xtan(1-sqrt(x))-(x^{3/2}sec^2(-sqrt(x)+1))/2)