What is the derivative of 4(x^2+5x+2tan(-x)) ?

The derivative of 4(x^2+5x+2tan(-x)) is -4(sec^2(x)(2+x^2+5x)+(2x+5)tan(x))

What is the first derivative of 4(x^2+5x+2tan(-x)) ?

The first derivative of 4(x^2+5x+2tan(-x)) is -4(sec^2(x)(2+x^2+5x)+(2x+5)tan(x))

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\frac{d}{d x} (4 (x^{2} + 5 x + 2) tan (- x))

- 4 (sec^{2} (x) (2 + x^{2} + 5 x) + (2 x + 5) tan (x))

Solution steps

\frac{d}{d x} (4 (x^{2} + 5 x + 2) tan (- x))

Simplify

4 (x^{2} + 5 x + 2) tan (- x) : - 4 tan (x) (2 + x^{2} + 5 x)

= \frac{d}{d x} (- 4 tan (x) (2 + x^{2} + 5 x))

Take the constant out:

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

= - 4 \frac{d}{d x} (tan (x) (2 + x^{2} + 5 x))

Apply the Product Rule:

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

f = tan (x), g = 2 + x^{2} + 5 x

= - 4 (\frac{d}{d x} (tan (x)) (2 + x^{2} + 5 x) + \frac{d}{d x} (2 + x^{2} + 5 x) tan (x))

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

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

= - 4 (sec^{2} (x) (2 + x^{2} + 5 x) + (2 x + 5) tan (x))

\frac{\partial}{\partial x} (2 x^{0.5} + y)

(x + 1) \frac{d y}{d x} + x y = ln (x)

f (x) = 8 x e^{x} csc (x)

\frac{d}{d x} (7 x)

\int_{6}^{8} \frac{40}{( x - 6 ) ^{3}} d x

What is the derivative of 4(x^2+5x+2tan(-x)) ?
The derivative of 4(x^2+5x+2tan(-x)) is -4(sec^2(x)(2+x^2+5x)+(2x+5)tan(x))
What is the first derivative of 4(x^2+5x+2tan(-x)) ?
The first derivative of 4(x^2+5x+2tan(-x)) is -4(sec^2(x)(2+x^2+5x)+(2x+5)tan(x))