What is the derivative of {f}(x(4sin(x^2-1))) ?

The derivative of {f}(x(4sin(x^2-1))) is 4(derivative of {f}(x)sin(x^2-1)+cos(x^2-1)*2x{f}(x))

What is the first derivative of {f}(x(4sin(x^2-1))) ?

The first derivative of {f}(x(4sin(x^2-1))) is 4(derivative of {f}(x)sin(x^2-1)+cos(x^2-1)*2x{f}(x))

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\frac{d}{d x} (f (x) (4 sin (x^{2} - 1)))

4 (\frac{d}{d x} (f (x)) sin (x^{2} - 1) + cos (x^{2} - 1) \cdot 2 x f (x))

Solution steps

\frac{d}{d x} (f (x) (4 sin (x^{2} - 1)))

Take the constant out:

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

= 4 \frac{d}{d x} (f (x) sin (x^{2} - 1))

Apply the Product Rule:

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

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

= 4 (\frac{d}{d x} (f (x)) sin (x^{2} - 1) + \frac{d}{d x} (sin (x^{2} - 1)) f (x))

\frac{d}{d x} (sin (x^{2} - 1)) = cos (x^{2} - 1) \cdot 2 x

= 4 (\frac{d}{d x} (f (x)) sin (x^{2} - 1) + cos (x^{2} - 1) \cdot 2 x f (x))

\int x^{2} x^{2} - 49 d x

\frac{d}{d x} (e^{x^{2} + 7 x})

\int_{0.2}^{0.4} 200 x d x

\int \frac{6}{( x ^{2} + 1 ) ^{\frac{3}{2}}} d x

f (x) = 9 π x^{2}

What is the derivative of {f}(x(4sin(x^2-1))) ?
The derivative of {f}(x(4sin(x^2-1))) is 4(derivative of {f}(x)sin(x^2-1)+cos(x^2-1)*2x{f}(x))
What is the first derivative of {f}(x(4sin(x^2-1))) ?
The first derivative of {f}(x(4sin(x^2-1))) is 4(derivative of {f}(x)sin(x^2-1)+cos(x^2-1)*2x{f}(x))