Computing directional derivatives with the gradient Compute the directional derivative of the following functions at the given point P in the direction of the given
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- Derivative rules Let u(t) = 2t3 i + (t2 - 1) j - 8 k and v(t) = et i + 2e-t j - e2t k. Compute the derivative of the following function. u(t) ⋅ v(t)arrow_forwardDerivatives of vector-valued functions Differentiate the following function. r(t) = ⟨4, 3 cos 2t, 2 sin 3t⟩arrow_forwardf(x,y)=3 e^x cos y, (a,b)=(0,π/4), and v⃗ =(2,3). Calculate the directional derivative of f at the point (a,b) in the direction defined by v⃗ . Find the direction at (a,b) in which the rate of change of f is greatest. Find the maximum rate of change. Fill in the blank: f decreases the most at (a,b) in the direction ofarrow_forward
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